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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.

Frequently Asked Questions

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