Calculation Examples

TOP/Calculation Examples

Free Calculator Input (Real Numbers)
Free Calculator Input (Complex Numbers)
Creating Graphs with Free Calculator
Precision Calculations

Free Calculator Input (Real Numbers) — Select "Real DEG"

Example

Input and Answer

Digits

Mode

Arithmetic

Expression10+20-30*4/6

Calculate

Answer10

Power

Expression3*4^2

Calculate

Answer48

Exponent

Expression99*1.23E+3

Calculate

Answer121770

Functions

Expressionsqrt(4)

Calculate

Answer2

Variables

Expressionsin(x)

Calculate

Variablex456

Calculate

Answer0.994522

Real DEG

Digit Change

Expressioncos(12345)

Calculate

Answer-0.258819

[Digits] 22

Calculate

Answer-0.2588190451025207623489

6
↓
22

Real DEG

Angle Change

Expressioncos(123456)

Calculate

Answer0.9135454576426008955021

[Mode] RAD

Calculate

Answer-0.6722948816565845196081

↓
Real RAD

Repeat Calc

Expressionsin(x)

Calculate

Variablex1, 0.1, 10

Calculate

Answer
1	0.8414709848078965066525
1.1	0.8912073600614353399518
1.2	0.9320390859672263496701
・・	・・
1.9	0.9463000876874144884897

Real RAD

Free Calculator Input (Complex Numbers) — Select "Complex RAD"

Example	Input and Answer	Digits	Mode
Arithmetic	Expression(3+4i)*(5+6i)CalculateAnswer-9 +38i	6	Complex RAD
Square Root √	Expressionsqrt(i)CalculateAnswer0.707107 +0.707107i	6	Complex RAD

Creating Graphs with Free Calculator

Example / Input	Mode	Graph and Settings
Square Root √ Expressionsqrt(x)Calculate Variablex0, 0.1, 51 CalculateGraph	6 Digits Real DEG	Width=190, Height=170, X skip=10
Trigonometric Expressionsin(x);cos(x)Calculate Variablex0, 5, 101 CalculateGraph	6 Digits Real DEG	Width=200, Height=170, Y Max=1 Min=-1, X skip=18
Normal Distribution Expressionnormalpd(x)Calculate Variablex-4, 0.1, 81 CalculateGraph	6 Digits Real DEG	Width=190, Height=170, Y Max=0.5 Min=0, X 10plot
Bessel Functions J₀(x), Y₀(x) Expressionbesselj(0,x);bessely(0,x)Calculate Variablex0, 0.1, 101 CalculateGraph	6 Digits Real DEG	Width=190, Height=180, Y Max=1 Min=-1

Precision Calculations (Pursuing accuracy with variable-digit technology)

Example	Mode	Keisan (6-digit) Precision
Example	Mode	Excel 2003 (16-digit)
Decimal Calc Expression0.4-0.3-0.1	6 Digits Real RAD	0.4-0.3-0.1 =0
Decimal Calc Expression0.4-0.3-0.1	6 Digits Real RAD	(0.4-0.3-0.1) =2.77556E-17 Binary-decimal conversion error
π Calculation Expressionsin(9*pi)	6 Digits Real RAD	sin(9*pi) =0
π Calculation Expressionsin(9*pi)	6 Digits Real RAD	SIN(9PI()) =1.10263E-15* π finite digitization error
Irrational Numbers 9√2-√162 Expression9*sqrt(2)-sqrt(162)	6 Digits Real RAD	9*sqrt(2)-sqrt(162) =0
Irrational Numbers 9√2-√162 Expression9*sqrt(2)-sqrt(162)	6 Digits Real RAD	(9SQRT(2)-SQRT(162)) =1.77636E-15* Irrational number finite digitization error
Complex Calc (1+i)⁴ Expression(1+i)^4	6 Digits Complex RAD	(1+i)^4 =-4
Complex Calc (1+i)⁴ Expression(1+i)^4	6 Digits Complex RAD	IMPOWER("1+i", 4) = -4 +4.89843E-16i
√(1+x)-1 x=1.23456E-100 Expressionsqrt(1+x)-1 Variablex1.23456E-100	6 Digits Real RAD	sqrt(1+ 1.23456E-100)-1 =6.1728E-101
	6 Digits Real RAD	SQRT(1+ 1.23456E-100)-1 =0 When x≪1, 1+x=1, no precision
e^ln(1+x)-1 x=1.23456E-14 Expressione^ln(1+x)-1 Variablex1.23456E-14	6 Digits Real RAD	e^ln(1+ 1.23456E-14)-1 =1.23456E-14
	6 Digits Real RAD	EXP(LN(1+ 1.23456E-14))-1 =1.24345E-14 When x≈1E-14, only 3 digits precision
e^ln(1+x)-1 x=1.23456E-15 Expressione^ln(1+x)-1 Variablex1.23456E-15	6 Digits Real RAD	e^ln(1+ 1.23456E-15)-1 =1.23456E-15
	6 Digits Real RAD	EXP(LN(1+ 1.23456E-15))-1 =0 When x<1E-15, no precision at all
Kinetic Energy E=mc²(1-√(1-v²/c²)) m=80kg v=100/9.77m/s c=299792458m/s Expressionmc^2(1-sqrt(1-v^2/c^2)) Variablem80 Variablev100/9.77 Variablec299792458	6 Digits Real RAD	m=80;v=100/9.77;c=299792458; mc^2(1-sqrt(1-v^2/c^2)) =4190.55
	6 Digits Real RAD	m=80;v=100/9.77;c=299792458; mc^2(1-SQRT(1-v^2/c^2)) =3991.274772 v≪c: Newton approx. E=mv²/2=4190.55

TOP/Calculation Examples