Shared Formulas (Science)

Calculating the thermal expansion of a substance when its temperature changes from one value to another

Calculate the turning radius based on ground speed and bank angle

It is well known that the boiling point of water decreases with increasing altitude; here, we will perform an approximate calculation.

Common to structural standards for pressure vessels (JIS, Specific Regulations for High-Pressure Gases, ASME, etc.) Calculation of the minimum required plate thickness for the shell and piping under internal pressure

Calculate the energy of a photon (in electronvolts) from the wavelength of light.

Calculate RPM from vehicle speed

We calculate the seismic moment and moment magnitude resulting from fault movement based on the fault area (fault length × fault width), average displacement, and stiffness.

Find the final velocity of the sphere.

Convert units of angular velocity

Calculate TAS (True Airspeed) using IAS (Indicated Airspeed) [kt], ISA Deviation [°C], and altitude [ft].

Calculate the magnetic field coefficients Nx, Ny, and Nz for the ellipsoid defined by x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. The double exponential integral formula (DE formula) is used for the calculation.

We will calculate the drag coefficient (CD) of a sphere using the Reynolds number (Re).

Bernoulli's Theorem (How to Calculate Dynamic Pressure)

This tool calculates the effective permittivity when powders or other materials are mixed into a medium (such as resin). It can calculate both the relative permittivity and tanδ.

Vertical throw (with air resistance)

Calculate the velocity from the particle's kinetic energy (in electronvolts).

This is a calculation of Einstein's equation: E=mc².

Calculate the sag of a catenary curve.

Converts the number of significant digits into a measure of standard deviation or standard error.

Find the minimum critical angle at which total internal reflection occurs when light is emitted from a medium into air.

Apparently, the reason the sound of pouring hot water sounds different from the sound of pouring cold water is that the viscosity of water varies significantly with temperature. Let’s take a look at a graph showing these temperature characteristics.

Raman shift, wavelength to Kaiser (excitation wavelength is arbitrary)

Common to structural standards for pressure vessels (JIS, Specific Regulations for High-Pressure Gases, ASME, etc.) Calculation of the minimum required plate thickness for a semi-circular mirror plate under internal pressure (pressure acting on the concave side)

Converts from Mach angle to Mach number.

Enter the thickness of the paper and the number of folds, and you'll see the thickness of the folded paper.

We will determine the terminal velocity of particles as small as raindrops.

This is the formula for calculating the stopping distance of a train.

Calculate the concentration of the gas

This calculates the frequency characteristics (dielectric dispersion) of the complex permittivity of water and ice. It explains why, in Nichirei’s chilled Chinese noodles, the water warms up but the ice does not. Please ignore the data showing ice at temperatures above 0°C and water at temperatures below 0°C.

Find the velocity of the sphere after an arbitrary time

When water from a flood or other source reaches the door, even if the water isn't very deep, the door will no longer open. Let's calculate the force acting on the door.

We will calculate the change in volume of a gas using the van der Waals equation of state.

Calculate the moment of inertia of a rectangular prism when the axis of rotation passes through its center of mass. a: Length of the rectangular prism in the x-direction b: Length of the rectangular prism in the y-direction c: Length of the rectangular prism in the z-direction M: Mass

Circumference = Radius * (2π); Angular velocity = (2π) * (Speed/Circumference); Centrifugal acceleration = Radius * (Angular velocity²);

Using the famous logistic map x_(n+1) = a*x_n*(1-x_n), which illustrates chaos, we will observe how the values diverge even with just a slight change in the initial conditions. You can choose from three different initial conditions. Calculations are performed with 50-digit precision.

Concentration Calculation

Find the coefficient of static friction when the angle of friction is θ.

Converts the temperature.

We will perform the calculation using the law of conservation of momentum. This calculation applies when both objects are moving along the same straight line. If the two objects are moving in opposite directions before the collision, set the pre-collision velocity of one of them to "negative."

Calculate the time taken, distance fallen, and kinetic energy for the free fall of an object subject to air resistance. (I modeled this after the "Free Fall with Air Resistance (Calculate from Time or Height)" formula in the physics formula collection.)

We calculate the energy levels of the hydrogen atom (Z=1) using the Dirac equation, which is the fundamental equation of relativistic quantum mechanics. We compare these results with those obtained from the non-relativistic Schrödinger equation.

　I would like to examine the function of a string suspended between two endpoints at different heights. Now, if we consider a function with one endpoint (which we’ll call the starting endpoint, while the other is the ending endpoint) as the origin, it is determined by the horizontal distance D between the endpoints, the height h of the ending endpoint, and the length L of the string, and is expressed as follows.Please note that in the following, cosh is the hyperbolic cosine function and is not the same as cos(h*...). *Since the aspect ratio of the generated graphs is generally not 1:1, if you wish to obtain a graph that closely resembles reality, please use the values of a and x1 shown in the first row of the table, along with the following equation, to plot the graph using graphing software or similar tools.

Electrons per atomic mass unit = Electrons generated / (Fuel 1 + Fuel 2); // From 1 [kg] = 1.6605402 * 10^27 [u] Atomic mass per gram = 10^24 / 1.6605402; Electron volts per gram = Electron volts per atomic mass * Atomic mass per gram; // Converting from 1 [J] = 1.60217733 / 10^19 [eV] to MeV Joules per electron volt = 1.60217733 / 10^(19-6); // Answer Joules per gram = electron volts per gram * joules per electron volt; Gigajoules per gram = joules per gram / 10^9;

Conversion between kilojoules and TNT

Calculate the velocity, constant deceleration, and constant decelerating force of a freely falling object

The calculation is based on the density of hydrogen under standard conditions (0°C, 101,325 Pa), which is 0.0899 kg/m³.

Building Services Engineering, Radiative heat transfer, Infinite parallel planes, Gray body, Black body, Stefan-Boltzmann coefficient, Emissivity, Mitake Michio

Convert standard deviation and standard error into a measure of significant digits.

Horizontal Projection of an Object

Calculate the time it takes for the water to reach a certain temperature.

We will calculate the force of universal gravitation. Using the gravitational constant G, mass M, mass m, and distance r, we will calculate the magnitude of the force f. Note that we have multiplied by -1 here to indicate that this is a gravitational force.

Diagonal projection; solvable

Find the speed v (m/s) of an object moving in uniform linear motion over a distance x (m) in a time t (s).

Find the delay in the Earth's rotation.

Viscosity Calculation

Calculate gravitational acceleration using mass and radius.

Conversion between frequency and relaxation time, and between temperature and inverse temperature

For calculating morph values in the PMX model of Newton's cradle. Enter an angle θ to obtain the vertical and horizontal amplitudes when the radius is set to 1.

Raman shift from the Kaiser (excitation wavelength is arbitrary)

The wave number of propagating surface plasmon polaritons excited by edge structures at the thin-film–metal interface

This is the formula for calculating the Young's modulus. Please use this when conducting experiments to determine the Young's modulus on 2B. Date Created: September 17, 2022

Combined drop-and-capillary method

Calculate the lift coefficient using lift, density, flow velocity, and the area of the control surface

The drag coefficient is calculated based on drag, density, flow velocity, and the representative area.

Calculate the actual length of a line (string) supported at two points horizontally.

The wavelength of propagating surface plasmon polaritons excited by edge structures on a metal surface

Calculate the time it takes for the air to reach a certain temperature

Have you ever found yourself wondering, "I think I could jump over this river..."? That's when this formula comes in handy! If you know the length of the river, you can instantly figure out how fast you need to jump to clear it! Plus, it works even if the river is sloped.

The free fall of a 1-kilogram object thrown horizontally from a specified height above the Earth's surface to sea level

Summer homework, assignments due, application forms, research progress—people tend to put all of these off until the very last minute. Tomasz Durakiewicz has proposed a theoretical formula, "A Universal Law of Procrastination," based on real-world examples that applies to all of these situations. It was also featured on Fermat's Library.

Calculate the time and speed required for an object moving at speed v to catch up with another object moving at acceleration a after t seconds

We will calculate the equivalent spring constant. Assume that the springs are connected in either a series or parallel configuration. We will consider up to 10 springs in the system.

We will determine two values: the limiting terminal velocity when rotating a non-tapered string, and the minimum mass ratio between the object and the string when rotating an object with a tapered string.

adiabatic process

The Holtzmark distribution describes the distribution of stars when they are randomly distributed in three dimensions, as observed from a single point under the influence of gravity.

E1 photon number in the HI collision imparted to the projectile

Enter the length l to calculate the period.

Only incandescent bulbs can be calculated

Convert from Celsius (°C) to Kelvin (K)

Schwarzschild radius

For objects moving at speeds close to the speed of light, time passes more slowly than for objects at rest. We calculate how much time has elapsed for the moving object relative to itself.

E1: Photon number from Betulani-Bauer Eq. 2.5.5.a

Assume that the S and S' reference frames are in translational motion relative to the x and x' axes. At t = 0, the origins coincide. The form of the transformation equations is: t' = (t − (v/(c²))x) / √(1 − (v/c)²) x' = (x - vt) / √(1 - (v/c)²) y' = y z' = z Let us assume this. In the S frame, the positive direction of v is toward x = +∞. c is the speed of light. (Input range: non-zero positive values)

adiabatic process

Disassembly time

We will calculate motion taking resistance into account (such as air resistance). Consider the x-y plane. The x-axis is horizontal, and the y-axis is vertical. Let the magnitude of the acceleration due to gravity be g, and define the side where y = -∞ as "down." The object starts at the origin (0,0) with an initial velocity v. Let θ be the angle at which it is "thrown." We will consider cases where the "drag" (drag coefficient divided by mass) acts in the opposite direction of velocity and is proportional to velocity.

We will calculate the equivalent mass. This is a system consisting of two particles.

Assume that the x, y, z, and ct axes of the S0 system are parallel to the x', y', z', and ct' axes of the S1 system. Multiply t and t' by c to convert the units to [m]. Calculate the transformation for a general velocity vector V.

We will calculate uniform accelerated motion.

This program calculates the formula for uniformly accelerated motion. This formula relates to coordinates. Let the coordinate be x. The direction of velocity toward +∞ is considered positive. The program outputs the coordinate x after t seconds of uniformly accelerated motion with acceleration a. The rest is for reference.

Convert frequency to period

Convert cycles to frequency

We use Snell's law to calculate the angle of emergence (angle of deviation) from the angle of incidence in air to the medium.

We use Snell's law to calculate the angle of refraction (the angle between the incident angle in the medium and the angle of emergence into air).

Determine the natural frequency of the first mode based on the string's tension, length, diameter, and density.

Calculate the distance-dependent attenuation of sound pressure levels for point and line sources.

Converts energy (eV) to wavelength (nm).

Converts frequency [Hz] to wavelength [m].

AC waveform (sine wave)

This graph illustrates the principle behind pulse oximeters—which gained attention during the COVID-19 pandemic—by showing the wavelength-dependent difference in the molar extinction coefficients between hemoglobin bound to oxygen (HbO₂) and hemoglobin that has released oxygen (Hb) (Please press the "Calculate" button first, then the "Graph" button).

Angle of incidence on the bonding surface of a 45-degree right-angle prism

Listen to the frequency of the siren sound and calculate how fast the ambulance is moving away. Assume the speed of sound is 340 m/s.

Calculate the frequency.

Convert the sound pressure unit from dB/mW to dB/Vrms. The impedance is that of the connected audio output device.

Determine the SPP and the beat wavelength of light

Calculate the frequency in the Pythagorean tuning system based on the note A1.

Determine the distance to where the lightning struck

The reflectance of light incident on the surface of glass from the air at an angle of incidence s1

Determine the SPP and the beat wavelength of light

The reflectance of light incident on the surface of glass from the air at an angle of incidence s1

Eyeglass lens prescription: diopter = dpt = D = SPH Lens focal length: focus mm Lens magnification: Magnification relative to the minimum focal length of 250 mm (0.25 m) for an adult with uncorrected vision

Determine the transposition and tuning based on the tempo value.

Given a lens with a diameter D, a refractive index N, and a power of SPH, where the radii of curvature R on both surfaces are equal, determine the focal length f and: the radius of curvature R and central thickness t of a convex lens, or the radius of curvature R and peripheral thickness of a concave lens.

Formula for calculating voltage from the wavelength of an LED

Formula for Calculating Wavelength from LED Voltage

We will calculate the upper limit of the resolution in an astronomical spectrograph as a function of slit width.

Calculate the distance to the image using the focal length f and the distance a to the object

Given a lens with a diameter D, a refractive index N, and a focal length f, where the radii of curvature R on both surfaces are equal, determine the radius of curvature R and the central thickness t for a convex lens, or the radius of curvature R and the peripheral thickness for a concave lens.

Calculate the distance to the image using the focal length f and the distance a to the object

Calculates the wavelength, reflectivity, transmittance, half-power depth, and skin depth of electromagnetic waves. The reflectivity and transmittance values are for light incident perpendicularly from air into the medium.

Wien's displacement law

Calculate the inductance, stray capacitance, and self-resonant frequency of an air-core inductor (coil) (see the blog below for details) https://laphroaig.blog.jp/archives/2011729.html You can perform calculations that take relative permeability into account at the link below. https://keisan.site/exec/user/1708128168

Following the ke!san post below, here are the calculations for a cylindrical coil that take relative permeability into account.<\n\ https://keisan.site/exec/user/1708117236

We will calculate the inductance, stray capacitance, and self-resonant frequency of a circular loop coil (see the blog below for details) https://laphroaig.blog.jp/archives/2011729.html

Attenuation of Radio Waves in Free Space

We will calculate Coulomb's law (in a vacuum). Let the equation be: F = (Q1 * Q2) / (4 * π * ε0 * (r^s)) [N] where π is the mathematical constant, ε0 is the permittivity of free space [C²/(N*m²)], and r is the distance [m]. s is an exponent.

Calculate the equivalent input noise voltage and the signal-to-noise ratio.

k = 1/sqrt(1 + (L/(2*R))^2) k2 = k^2 Kn = (4/(3*pi*sqrt(1-k2)) * (((1-k2)/k2) * ellipticK(k) - ((1-2*k2)/k2) * ellipticE(k) - k))

Calculate the conversion efficiency and losses.

the self-capacitance of a conducting sphere of radius R

We determine the frequency or wavelength of electromagnetic waves within a material based on its relative permittivity and relative permeability.

It can be used for thermal design of MOSFETs and similar components.

Assuming the Earth’s thermal conductivity is infinite and its thermal resistance is zero, the equation explained by Hansen, based on solar radiation and blackbody radiation, shows that without greenhouse gases, the Earth’s surface temperature would drop to -18°C. Science, August 23, 1981 issue Te = [So(1 - A)/4σ]^(1/4)

Calculate the saturation current and inductance with and without a gap

Power density, electric field, magnetic field, and magnetic flux density at a vacuum impedance of 120π = 377 Ω

Assuming the Earth’s thermal conductivity is infinite and its thermal resistance is zero, the equation explained by Hansen, based on solar radiation and blackbody radiation, shows that without greenhouse gases, the Earth’s surface temperature would drop to -18°C. Science, August 23, 1981 issue Te = [So(1 - A)/4σ]^(1/4)

Substitute the values of each metal below for K.

Assuming the Earth’s thermal conductivity is infinite and its thermal resistance is zero, the equation explained by Hansen, based on solar radiation and blackbody radiation, shows that without greenhouse gases, the Earth’s surface temperature would drop to -18°C. Science, August 23, 1981 issue Te = [So(1 - A)/4σ]^(1/4)

Convert the mass percentage concentration of hydrochloric acid to molar concentration.

Convert the mass percentage concentration of sulfuric acid to molar concentration.

Calculate the mass of potassium aluminum sulfate dodecahydrate required to dissolve in 100 g of water.

Convert the mass percentage concentration of sodium hydroxide to molar concentration.

You can calculate the pH of a very dilute acid where the ionization of water can no longer be ignored. The ionic product of water is assumed to be Kw = 1.0E-14 (mol/L)² at 25°C. Please enter the concentration (mol/L) and the valence.

Convert the mass percentage concentration of nitric acid to molar concentration.

Calculate the pH based on the amount of sodium hydroxide used.

Given the pH of an aqueous solution, determine the pH of the solution after diluting it with water by a certain factor.

This graph illustrates the steady-state conditions following a single dose and repeated doses administered at regular intervals up to four times a day.

You can calculate the pH of a very dilute base where the dissociation of water can no longer be ignored. We assume the ionic product of water at 25°C to be Kw = 1.0E-14 (mol/L)². Please enter the concentration (mol/L) and valence.

Calculate the mass of sodium hydroxide required to dissolve in 100 g of water.

Calculate the pH based on the amount of hydrochloric acid used.

《High-Speed Version》pH Calculation Simulates acid-base titrations of polybasic acids, polybasic bases, and mixtures. To improve speed, the horizontal axis represents pH and the vertical axis represents volume.

pH change in a buffer solution (weak acid + strong base)

Calculate the mass of hydrochloric acid that dissolves in 100 g of water.

Convert the units of energy and calculate the difference. Please enter two energy values in hartree units.

Divide the reaction current by the electrode area to calculate the current density.

pH Calculator Mini (Divalent, Trivalent, and Mixtures) Simulates acid-base titrations involving polyprotic acids, polyprotic bases, and mixtures.

Calculate the hydroxyl valence based on the molecular weight and the number of hydroxyl groups.

Calculate the formulation weight based on the isocyanate concentration (NCO%) and hydroxyl value.

The relationship between temperature and energy differences and the enantiomeric excess (Celsius version)

pH Calculations (Divalent to Pentavalent, Mixtures) Simulates acid-base titrations involving polyvalent acids, polyvalent bases, and mixtures.

pH change in a buffer solution (weak base + strong acid)

a

This is for calculating hot spring concentrations on the bulletin board.

The relationship between temperature and energy differences and the enantiomeric excess (Celsius version)

We estimate the reaction rate constant using the Eyring equation: k = ΓkBT/h * exp(-ΔG²/RT) In addition, we estimate the time constant and the reaction time. We neglect the tunneling effect and assume the transmission coefficient Γ = 1.

Calculate the formulation weight based on the epoxy equivalent weight and hydroxyl value.

Calculation of the Helical Excess Ratio

Formula for calculating NMR yield

Tafel's formula

Estimating the energy difference roughly based on the g-value

We estimate the reaction rate constant using the Eyring equation: k = ΓkBT/h * exp(-ΔG²/RT) In addition, we estimate the time constant and the reaction time. We neglect the tunneling effect and assume the transmission coefficient Γ = 1.

This is a formula for calculating the amounts of citric acid and baking soda based on the amount of carbon dioxide produced.

Determine the cell constant based on the electrode area and the distance between electrodes.

We calculate the reaction current from the reaction rate. This is calculated by multiplying the amount of substance reacting per unit time by the number of electrons involved in the reaction and Faraday's constant.

The relationship between the temperature-energy difference and the enantiomeric excess (absolute temperature version)

Prepare a solution of a given mole fraction in terms of weight concentration

Given the partial pressure of carbon dioxide (pCO₂) and the dissolved inorganic carbon (DIC) concentration in the atmosphere, calculate the pH of seawater.

Please enter your scores. Although there may be a bug where the course names do not display, please enter them in the following order: Organic Chemistry 2: Structural Theory Chemical Thermodynamics 2 Quantum Chemistry 2 Solid-State Chemistry Organic Chemistry 3: Reaction Theory Structural Chemistry Inorganic Chemistry Radiochemistry Chemical English

Relationship Between the Number of Chiral Units and the Helical Excess (Graph Version)

Calculate the mass of active material based on the battery capacity.

Suppose there is M [g] of a saltwater solution with a concentration of n%. Calculate the mass of salt [g] and the mass of water [g] in this solution.

Practical pH Calculations (Amphoteric Electrolytes) – Quartic Equation Function

Quartic Equation Function Calculating the pH of Sodium Bicarbonate (Baking Soda) Using a Quartic Equation Practical pH Calculations (Amphoteric Electrolytes)

The proportion of each carbonate component in total dissolved carbonates in water: [DIC] = a [H₂CO₃], [DIC] = b [HCO₃⁻], [DIC] = c [CO₃²⁻]

The proportion of each carbonic acid component relative to total carbonic acid at dissociation equilibrium (determines pH) The proportion of each carbonic acid component relative to total carbonic acid in water

Quartic Equation Function Calculating the pH of Sodium Bicarbonate (Baking Soda) Using a Quartic Equation Practical pH Calculations (Amphoteric Electrolytes)

Calculate the hydrogen ion concentration, pH, and total dissolved carbon dioxide (DIC) in rainwater (freshwater)

Prepare a solution of a given mole fraction in terms of weight concentration

Quartic Equation Function Calculating the pH of Sodium Bicarbonate (Baking Soda) Using a Quartic Equation Practical pH Calculations (Amphoteric Electrolytes)

Calculate the hydrogen ion concentration, pH, and total dissolved carbon dioxide (DIC) in rainwater (freshwater) Calculations based on a water temperature of 25°C

Calculate the hydrogen ion concentration, pH, and total dissolved carbon dioxide (DIC) in rainwater (freshwater) Calculations based on a water temperature of 5°C

The proportion of each carbonic acid component relative to total carbonic acid at dissociation equilibrium (determines pH) The proportion of each carbonic acid component relative to total carbonic acid in water

Quartic Equation Function Calculating the pH of Sodium Bicarbonate (Baking Soda) Using a Quartic Equation Practical pH Calculations (Amphoteric Electrolytes)

Quadratic Equations Formula for the Roots (Full Version) – Simplified by substituting parts of the equation I used the formula from Wikipedia, but the result differs slightly from the official value. Highly likely a typo! I’d like to fix this someday! I tried fixing it by using the `cubicRoot(x1)` function, but it stopped running with an "Input Error"!

Calculate the hydrogen ion concentration, pH, and total dissolved carbon dioxide (DIC) in rainwater (freshwater) Calculations based on a water temperature of 5°C

Quartic Equation Function Calculating the pH of Sodium Bicarbonate (Baking Soda) Using a Quartic Equation Practical pH Calculations (Amphoteric Electrolytes)

Calculate the distance and angle to the horizon.

Calculating Camera Angle of View and Focal Length

We'll calculate the Drake Equation to determine how many planets host extraterrestrial life.

Calculate the azimuth (the difference between true north and the direction indicated by a compass). Please enter the latitude and longitude (ITRF coordinate system, GRS80 ellipsoid coordinates) of the location you wish to calculate.

We will calculate the energy required to shatter a star.

We calculate the energy released upon impact with Earth based on the meteorite's diameter, density, and velocity. Using the given values, we determine the meteorite's mass and calculate its kinetic energy.

Calculate the telescope's light-gathering power, resolution, limiting magnitude, and optimal magnification. Please enter the telescope's aperture.

We calculate the star's radius based on its surface temperature and spectral class (please note that errors may occur if the star is very luminous or located far from the main sequence on the HR diagram, so please use this information for reference only).

Converts the semi-major axis to an orbital period. This is useful for calculating the orbital periods of solar system bodies such as planets and asteroids.

Calculate the camera focal length based on the subject's size Calculations are based on 35mm format.

Calculating the camera's angle of view or focal length. Calculations are based on 35mm format.

Calculates the size of the Airy disk on the image plane based on the lens aperture and focal length.

Schwarzschild Radius Calculator\n The Schwarzschild radius is the size of a massive object at which the escape velocity—the speed required to break free from its gravitational pull—is greater than or equal to the speed of light. Simply put, it is used to calculate the size (radius) of a massive object when it becomes a black hole.

Convert UTC to LST (Local Sidereal Time)

Calculate the correction value (ΔT) for the Earth's rotational speed

Calculate ΔV based on the rocket's initial mass, final mass, and specific impulse

Calculate the azimuth and elevation as seen from an observation point at a specific location along the rocket's orbit.

We’ll calculate what aperture size is needed to observe an nth-magnitude star. Please use this as a reference for selecting a telescope, as aperture size is a key factor.

Calculate the maximum exposure time required to capture stars as point sources without equatorial tracking.

We will calculate the area required for solar power generation for a lunar mass driver. The lunar escape velocity (the speed required to break free from the Moon’s gravity) is 2378 [m/s]. The energy required to accelerate 1 ton to this speed is: 1000 * 2378^2 / 2 = 2827442000 [J]. The solar energy available at Earth’s orbital altitude, based on the solar constant of 1366 [W/m²], results in an annual energy of: 1366 * (60*60*24*365.2422) = 43106761025.28 [J/m²]. From this, we can calculate the required area for solar power generation.

Calculate the Julian day down to the hour, minute, and second

Find the radius of a geostationary orbit around a star of a given mass. It is assumed that the mass of the orbiting body is sufficiently small compared to that of the star at the center of rotation. Since the calculated result is the radius from the star’s center of mass, please subtract this value as appropriate when calculating the distance from the star’s surface.

Calculate the orbital radius (Hill sphere) at which a body can remain a satellite of a planet.

Convert LST (Local Sidereal Time) to UTC

Calculate the distance between two points in celestial coordinates. Longitude is expressed in hours (0–24), minutes, and seconds; latitude is expressed in degrees, minutes, and seconds.

This calculates the gravitational acceleration inside and outside the Earth using the PREM (Preliminary Reference Earth Model). It’s interesting to note that in some places, g is greater inside the Earth than at the surface.

This figure illustrates the density distribution of the Earth's interior based on the PREM (Preliminary Reference Earth Model).

Calculate the final mass based on the rocket's initial mass, ΔV, and specific impulse

Calculate the velocity required for an object to become a satellite

Schwarzschild radius

Relativistic perihelion shift

Calculate the dew point temperature from the air temperature and relative humidity

Calculate an approximate value for the saturated vapor pressure.

Air Density and Kinematic Viscosity

Calculating vapor pressure from temperature

Calculate the potential temperature from temperature and atmospheric pressure; and perform the inverse calculation

Calculate the sea-level equivalent pressure

Calculate the SSI based on temperature and humidity

Determining wind direction and speed from wind components, or vice versa

Calculate vorticity

Calculate the lifting condensation altitude from the parameters

The Relationship Between the Number of Times Crickets Chirp and Air Temperature

Calculate convergence and divergence

US Standard Atmosphere 1976 h -6,000 m to +20,000 m

This graph shows the average annual data for typhoons. The horizontal axis represents the months (January–December), and the vertical axis shows the average annual numbers of typhoons that form, approach the coast, and make landfall.

Kayanuma Water Level Calculation

The decay curve of atmospheric CO₂ as defined by the IPCC

This graph shows the ratio of typhoon activity relative to the long-term average. The horizontal axis represents the months (1–12), and the vertical axis shows three values: (number of approaches / number of occurrences) × 100%, (number of landfalls / number of occurrences) × 100%, and (number of landfalls / number of approaches) × 100%.