Last updated
Scientific Calculator Examples
The Scientific Calculator handles trigonometry, logarithms, exponentials, statistics, complex numbers, and more. Below are examples of common calculations.
Basic Arithmetic with Operator Precedence
Expression: 2 + 3 × 4
Result: 14 (multiplication before addition)
Expression: (2 + 3) × 4
Result: 20 (parentheses first)
Expression: 2^10
Result: 1024
Expression: √144
Result: 12
Expression: ∛27
Result: 3
Trigonometric Functions — Degree Mode
sin(30°) = 0.5
cos(60°) = 0.5
tan(45°) = 1
sin(90°) = 1
cos(180°) = -1
Inverse functions:
arcsin(0.5) = 30°
arccos(0.5) = 60°
arctan(1) = 45°
Trigonometric Functions — Radian Mode
sin(π/6) = 0.5
cos(π/3) = 0.5
tan(π/4) = 1
sin(π/2) = 1
cos(π) = -1
Expression: sin(π/4)^2 + cos(π/4)^2
Result: 1 (Pythagorean identity)
Logarithms and Exponentials
Natural logarithm:
ln(e) = 1
ln(1) = 0
ln(100) = 4.6052
Base-10 logarithm:
log(10) = 1
log(100) = 2
log(1000)= 3
Exponential:
e^1 = 2.71828
e^2 = 7.38906
10^3 = 1000
Inverse relationship:
e^(ln(5)) = 5
ln(e^3) = 3
Factorial and Combinations
Factorial:
5! = 120
10! = 3,628,800
0! = 1
Combinations (n choose k):
C(10, 3) = 10! / (3! × 7!) = 120
C(52, 5) = 2,598,960 (poker hands)
Permutations:
P(10, 3) = 10! / 7! = 720
Hyperbolic Functions
sinh(1) = 1.1752
cosh(1) = 1.5431
tanh(1) = 0.7616
Identity: cosh²(x) - sinh²(x) = 1
cosh²(1) - sinh²(1) = 1.5431² - 1.1752² = 1 ✓
Statistical Functions
Calculate statistics for a dataset:
Dataset: 12, 15, 18, 22, 25, 28, 31, 35
Mean: 23.25
Median: 23.5
Mode: (no mode — all values unique)
Range: 23 (35 - 12)
Variance: 52.44
Standard deviation: 7.24
Min: 12, Max: 35
Complex Numbers
Addition:
(3 + 4i) + (1 + 2i) = 4 + 6i
Multiplication:
(3 + 4i) × (1 + 2i) = 3 + 6i + 4i + 8i²
= 3 + 10i - 8
= -5 + 10i
Magnitude (modulus):
|3 + 4i| = √(3² + 4²) = √25 = 5
Polar form:
3 + 4i = 5∠53.13°
Euler's formula:
e^(iπ) + 1 = 0
Number Base Conversion (Programmer Mode)
Decimal 255:
Binary: 11111111
Octal: 377
Hexadecimal: FF
Decimal 42:
Binary: 101010
Octal: 52
Hexadecimal: 2A
Bitwise operations on 12 (1100) and 10 (1010):
AND: 1100 & 1010 = 1000 = 8
OR: 1100 | 1010 = 1110 = 14
XOR: 1100 ^ 1010 = 0110 = 6
NOT: ~1100 = ...11110011 (two's complement)
Matrix Operations
Matrix A: Matrix B:
[2 3] [1 0]
[1 4] [2 3]
A × B:
[2×1+3×2 2×0+3×3] [8 9]
[1×1+4×2 1×0+4×3] = [9 12]
Determinant of A:
det(A) = (2×4) - (3×1) = 8 - 3 = 5
Inverse of A:
A⁻¹ = (1/5) × [4 -3] = [0.8 -0.6]
[-1 2] [-0.2 0.4]
Calculation History
Multi-step calculation using history:
Step 1: sin(30°) = 0.5
Step 2: cos(60°) = 0.5
Step 3: 0.5 + 0.5 = 1.0 (click previous results to reuse)
Step 4: √1.0 = 1.0
History shows all steps — click any result to use it in a new calculation.
- Trigonometric functions in degree or radian mode
- Logarithms (ln, log), exponentials, and power functions
- Factorial, combinations, and permutations
- Hyperbolic functions (sinh, cosh, tanh)
- Statistical functions: mean, median, standard deviation
- Complex number arithmetic and polar form conversion
- Number base conversion and bitwise operations (programmer mode)
- Matrix operations: multiplication, determinant, inverse