Scientific Calculator

About Scientific Calculator

This scientific calculator evaluates mathematical expressions containing trigonometric functions (sin, cos, tan), logarithms (log, ln), roots (sqrt), powers (^), and mathematical constants (π, e). It follows standard order of operations (PEMDAS) and accepts angles in degrees for trigonometric calculations.

It is useful for engineering calculations, physics problems, mathematics homework, chemistry computations, financial modeling, statistics work, and any technical field requiring scientific notation and advanced mathematical functions beyond basic arithmetic.

Supported Functions Reference

Complete list of available mathematical operations:

Trigonometric Functions (angles in degrees):
  sin(x)    - Sine of angle x in degrees
  cos(x)    - Cosine of angle x in degrees
  tan(x)    - Tangent of angle x in degrees
  asin(x)   - Arc sine, returns angle in degrees
  acos(x)   - Arc cosine, returns angle in degrees
  atan(x)   - Arc tangent, returns angle in degrees

Logarithmic Functions:
  log(x)    - Logarithm base 10 (common log)
  ln(x)     - Natural logarithm (base e)

Exponential Functions:
  exp(x)    - e raised to power x (e^x)
  10^x      - 10 raised to power x

Root Functions:
  sqrt(x)   - Square root of x
  cbrt(x)   - Cube root of x

Power Operation:
  x ^ y     - x raised to power y

Constants:
  pi, π     - 3.141592653589793...
  e         - 2.718281828459045...

Arithmetic Operators:
  + - * /   - Addition, subtraction, multiplication, division
  %         - Modulo (remainder)
  ()        - Parentheses for grouping

Example Expressions:
  sin(30) + cos(60)           = 0.5 + 0.5 = 1
  log(100)                    = 2
  ln(e)                       = 1
  sqrt(16) * 2                = 8
  2 ^ 8                       = 256
  pi * 5 ^ 2                  = 78.54 (circle area)
  (2 + 3) * 4                 = 20

Order of Operations (PEMDAS)

Expressions are evaluated following standard mathematical precedence:

Precedence Order (highest to lowest):

1. Parentheses ()
   - Innermost evaluated first
   - (2 + 3) * 4 = 5 * 4 = 20

2. Functions and Exponents
   - sin(30), sqrt(16), 2^3
   - 2^3 + 1 = 8 + 1 = 9

3. Multiplication and Division (*, /)
   - Left to right
   - 10 / 2 * 3 = 5 * 3 = 15

4. Addition and Subtraction (+, -)
   - Left to right
   - 10 - 3 + 2 = 7 + 2 = 9

Common Mistakes:

  2 + 3 * 4     = 14  (NOT 20)
  (2 + 3) * 4   = 20  (parentheses change order)

  8 / 2 * 2     = 8   (NOT 2)
  8 / (2 * 2)   = 2   (parentheses required)

  2 ^ 3 ^ 2     = 512 (right to left: 3^2=9, then 2^9=512)
  (2 ^ 3) ^ 2   = 64  (left to right: 2^3=8, then 8^2=64)

Trigonometric Function Values

Logarithm Properties

Logarithm Rules:

Product Rule:
  log(a × b) = log(a) + log(b)
  Example: log(1000) = log(10 × 100) = log(10) + log(100) = 1 + 2 = 3

Quotient Rule:
  log(a / b) = log(a) - log(b)
  Example: log(100/10) = log(100) - log(10) = 2 - 1 = 1

Power Rule:
  log(aⁿ) = n × log(a)
  Example: log(1000) = log(10³) = 3 × log(10) = 3 × 1 = 3

Change of Base:
  log_b(x) = log(x) / log(b)
  Example: log₂(8) = log(8) / log(2) = 0.903 / 0.301 ≈ 3

Common Logarithm Values (base 10):
  log(1)      = 0
  log(10)     = 1
  log(100)    = 2
  log(1000)   = 3
  log(0.1)    = -1
  log(0.01)   = -2

Natural Logarithm Values (base e):
  ln(1)       = 0
  ln(e)       = 1
  ln(e²)      = 2
  ln(10)      ≈ 2.303

Mathematical Constants

Example Calculations

Geometry:
  Circle area (r=5):     pi * 5^2 = 78.54
  Circle circumference:  2 * pi * 5 = 31.42
  Sphere volume (r=3):   (4/3) * pi * 3^3 = 113.10
  Triangle area (b=10,h=6):  0.5 * 10 * 6 = 30

Physics:
  Kinetic energy (m=10,v=5):  0.5 * 10 * 5^2 = 125
  Force (m=5,a=9.8):     5 * 9.8 = 49 N
  Wave frequency (T=0.02):  1 / 0.02 = 50 Hz
  Pendulum period (L=1):  2 * pi * sqrt(1/9.8) ≈ 2.01 s

Finance:
  Compound interest (P=1000,r=5%,t=10):  1000 * (1.05)^10 = 1628.89
  Present value (FV=1000,r=5%,t=5):  1000 / (1.05)^5 = 783.53

Statistics:
  Z-score (x=85,μ=75,σ=10):  (85-75) / 10 = 1.0
  Standard deviation sample: sqrt(Σ(x-μ)²/(n-1))

Trigonometry:
  Right triangle (θ=30°,hyp=10):
    opposite = 10 * sin(30) = 5
    adjacent = 10 * cos(30) = 8.66

Scientific Notation

Scientific Notation Format:
  a × 10ⁿ where 1 ≤ |a| < 10

Examples:
  Speed of light:     299,792,458 m/s = 2.998 × 10⁸ m/s
  Planck constant:    6.626 × 10⁻³⁴ J·s
  Avogadro's number:  6.022 × 10²³ mol⁻¹
  Earth mass:         5.972 × 10²⁴ kg
  Electron charge:    1.602 × 10⁻¹⁹ C

Calculator Input:
  Use 'e' notation: 2.998e8 = 299,792,458
  6.022e23 = 602,200,000,000,000,000,000,000
  1.602e-19 = 0.0000000000000000001602

Note: In this calculator, 'e' alone represents
Euler's number. Use 'e' notation only in the
form XeY where X and Y are numbers.

Common Formulas Reference

Error Conditions

• Division by zero: Expressions like 1/0 return "Infinity" or "Error"
• Negative square root: sqrt(-1) returns "NaN" (not a number) for real-valued calculations
• Invalid syntax: Missing parentheses or malformed expressions show "Error: Invalid"
• Domain errors: log(0), log(negative), asin(>1), acos(>1) return "NaN" or "Infinity"
• Overflow: Extremely large results (10^1000) return "Infinity"
• Underflow: Extremely small results may round to 0