Author: kegasa

cubic_equation_formula

cubic_equation_formula

cubicEquation function

cubicEquation function

Quadratic Equation Function

Quadratic Equation Function

Solving Quadratic Equations in Excel

A formula that calculates the roots of a quartic equation just by pasting it into an Excel cell

Isothermal compression and isothermal expansion, using 1 cubic meter of nitrogen at 0°C and 1 atmosphere as the reference

adiabatic process

What happens if you fill a 1-meter-square cube with nitrogen at 1 atmosphere of pressure and compress it with a weight?

adiabatic process

Schwarzschild radius

Schwarzschild radius

Snell's and Fresnel's Formulas (Fresnel) Table

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

Snell's and Fresnel's laws (Fresnel) graph

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

Formula for Calculating Wavelength from LED Voltage

Formula for Calculating Wavelength from LED Voltage

Formula for calculating voltage from the wavelength of an LED

Formula for calculating voltage from the wavelength of an LED

Diopter, Focal Length, and Magnification in Eyeglasses

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

Calculating the radius of curvature and thickness of a lens based on its focal length and refractive index

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 focal length, radius of curvature, and thickness of a lens based on the prescription strength and refractive index

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.

Calculate the image distance based on the lens focal length and the distance from the object

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

Calculate the image distance and magnification based on the lens focal length and the distance from the object

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

Table of Nagaoka Coefficients (R = Coil Radius, L = Coil Length)

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))

Peak wavelength of blackbody radiation (Wien's displacement law)

Wien's displacement law

The capacitance of a sphere of radius r

the self-capacitance of a conducting sphere of radius R

Received signal strength

Attenuation of Radio Waves in Free Space

Calculating the surface temperature of Earth without the greenhouse effect using Hansen's equation

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)

Calculating the surface temperature of a regular tetrahedron using Hansen's formula from NASA

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)

Calculating the surface temperature of a sphere using Hansen's formula from NASA

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)

Field Strength Conversion

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

Quadratic Equations: Needs correction!

Quadratic Equations Formula for Solutions (Full Version)—Simplified by substituting parts of the equation I used the formula from Wikipedia, but the result differs slightly from the value given in the formula.

Calculate the pH of rainwater (freshwater) (carbon dioxide is in equilibrium between the atmosphere and rainwater)

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

Determine the pH of seawater

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

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

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

Table showing the proportion of each carbonate component relative to total carbonates in water

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

Graph showing the proportion of each carbonate component in total carbonates in water

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

Calculating the pH of sodium bicarbonate (baking soda) using a quartic equation

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

Plotting the pH of sodium bicarbonate (baking soda) using a quartic equation

Practical pH Calculations (Amphoteric Electrolytes) – Quartic Equation Function

Calculating the pH of sodium bicarbonate (baking soda) using a quartic equation, including pCO₂

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

Calculate the pH of rainwater (freshwater) (carbon dioxide is in equilibrium with the atmosphere) at 25°C

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

Calculating the pH of sodium bicarbonate (baking soda) using a fourth-degree equation at 25°C

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

Calculating the pH of sodium bicarbonate (baking soda) using a quartic equation at 40°C

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

Calculate the pH of rainwater (freshwater) (carbon dioxide is in equilibrium with the atmosphere) at 5°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

Calculate the pH of rainwater (freshwater) (carbon dioxide is in equilibrium with the atmosphere) at 40°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

Calculating the pH of sodium bicarbonate using a quartic equation, with pCO₂ at 40°C

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

Schwarzschild radius: not specified

Schwarzschild radius

The Relationship Between Altitude, Temperature, and Air Pressure

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

The decay curve of atmospheric CO₂ as defined by the IPCC

The decay curve of atmospheric CO₂ as defined by the IPCC

Inductance of a cylindrical coil (R = radius, L = length, N = number of turns)

Inductance of a circular loop antenna (radius R, length L) S = πR²; Lcoil = Kn * ur * μ₀ * S * N² / L * 10⁶;

The Nagaoka coefficient Ks and inductance L of a square loop antenna

square loop antenna (side a = p, side b = p) L Rr Rac η

The Skin Effect and the Resistance of Circular Copper Wire

Skin depth of copper and resistance of round wire

Inductance of a single-turn circular loop coil

Self-inductance of a thin wire Circular loop

Inductance of a rectangular coil (b × d)

Self-inductance of a rectangle made of round wire

Short wire antenna h Ra Xc η

Short Vertical Antenna height, diameter Ra radiation

Aluminum Wire: Diameter, Length, Weight, Resistance, and AC Resistance (Skin Effect)

Aluminum Wire Length and Diameter for Rdc Rac Weight

Cylindrical coil μH (R = radius, L = length, N = number of turns) CD50

Inductance of a circular loop antenna (radius R, length L) S = πR²; Lcoil = Kn * ur * μ₀ * S * N² / L * 10⁶;

LC resonant circuit

LC resonant circuit to measure capacitance

Magnetic susceptibility of a rotating ellipsoid

Demagnetizing factor of an ellipsoid

Magnetic susceptibility of an ellipsoid

Demagnetizing factor of an ellipsoid

Equivalent Impedance of an LC Parallel Resonant Circuit

Equivalent Impedance of an LC Parallel Resonant Circuit

Gain of a Dipole Antenna

Gain of a dipole antenna

Calculate power density and electric field strength from transmit power and antenna gain

Antenna Gain, Transmit Power, Distance to E, H, B

Equivalent impedance of an LC parallel resonant circuit (μH)

Equivalent Impedance of an LC Parallel Resonant Circuit

Gain and Matching Coil for a Wire Antenna with a Wavelength < 0.1λ at 828 kHz

Short Vertical Antenna height, diameter Ra radiation

Equivalent impedance of an LC parallel resonant circuit at 828 kHz

Equivalent Impedance of an LC Parallel Resonant Circuit

Gain and Matching Coil for Wire Antennas with a Wavelength of 0.1λ or Less at 60 kHz

Short Vertical Antenna height, diameter Ra radiation

Determining the Resonance Frequency of an LC Resonator

Resonant frequency of an LC resonator

Impedance Converter (Matching Circuit)

Impedance Matching Z1:Z2 (R1:R2) Z1 > Z2 Z1 to Z2 matching using series R1 and parallel R2

Calculation of the Nagaoka Coefficient (R = coil radius, L = coil length) in meters

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))

Impedance Matching Network

Impedance Matching Network Rs in series, Ls in parallel, Cp, Rp

Converting E96-series notation for surface-mount chip resistors to resistance values

SMD Resistance Value Code\ E96 Series

The original method for calculating power density and electric field strength from transmit power and antenna gain

Antenna Gain, Transmit Power, Distance to E, H, B

Power Loss in Top-Runner Transformers Rated at 500 kVA or Less

Losses in Top Runner transformers rated at 500 kVA or less.

Sample 3 using a function: cubicRoot(x)

Sample 3 using functions\ cubicRoot(x)