Scientific Calculator
A free scientific calculator with full expression parsing for trigonometry (sin, cos, tan), logarithms (log base 10 and natural log), square roots, exponents, parentheses, π, and Euler's constant e. Type expressions directly using the on-screen button grid or your keyboard, and the calculator evaluates them following the standard PEMDAS / BODMAS order of operations — parentheses first, then exponents, then multiplication and division left-to-right, then addition and subtraction. Trigonometric functions take input in radians by default; convert degrees to radians with × π / 180 (for example, sin(30 * pi / 180) for sin 30°). The expression engine is powered by the mathjs library, which provides accurate IEEE-754 evaluation for the entire range of common math operations. The last five calculations are kept in history so you can re-run, edit, or chain results. Use this for physics homework, engineering quick checks, statistics work, financial formulas, or anywhere a basic four-function calculator is not enough.
How to Use This Calculator
- AC — clears the current expression and display
- ± — toggles the sign of the current number (positive/negative)
- % — adds a percent symbol to the expression
- sin, cos, tan — insert the function name and opening parenthesis (input in radians)
- √ — inserts sqrt( for square root
- x² — appends ^2 to square the current value
- xn — appends ^ so you can type any exponent
- log — inserts log10( (common log, base 10)
- ln — inserts log( (natural log, base e, mathjs notation)
- π — inserts the constant pi (≈ 3.14159)
- e — inserts Euler's number (≈ 2.71828)
Order of Operations (PEMDAS)
Expressions are evaluated following standard mathematical order of operations:
- P — Parentheses (innermost first)
- E — Exponents (right to left)
- MD — Multiplication and Division (left to right, equal priority)
- AS — Addition and Subtraction (left to right, equal priority)
Examples:
- 3 + 4 × 2 = 3 + 8 = 11 (not 14). For quick percentage problems, our Percentage Calculator is faster
- (3 + 4) × 2 = 7 × 2 = 14
- 232 = 29 = 512 (right-to-left for exponents)
- 10 ÷ 2 × 5 = 5 × 5 = 25 (left to right)
Trigonometric Functions
This calculator uses radians by default for trigonometric functions, matching the standard mathematical convention and most programming environments.
To calculate trig in degrees, multiply the angle by π/180 first: sin(45°) = sin(45 × pi/180) = sin(0.7854) ≈ 0.7071.
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 0.5 | 0.866 | 0.577 |
| 45° | π/4 | 0.707 | 0.707 | 1 |
| 60° | π/3 | 0.866 | 0.5 | 1.732 |
| 90° | π/2 | 1 | 0 | undefined |
| 180° | π | 0 | −1 | 0 |
Logarithm Quick Reference
- log10(x) — common logarithm (base 10). log10(1000) = 3 because 10³ = 1000.
- log(x) — natural logarithm (base e). log(e) = 1. log(1) = 0.
- Change of base: logb(x) = log(x) / log(b) = log10(x) / log10(b).
- Inverse (antilog): if log10(x) = 3, then x = 10³ = 1000. If log(x) = 2, then x = e² ≈ 7.389. Logarithms are key to compound interest calculations
Frequently Asked Questions
What is the order of operations?
Order of operations (PEMDAS/BODMAS): Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). For example, 3 + 4 × 2 = 3 + 8 = 11 (not 14). Use parentheses to override the default order: (3 + 4) × 2 = 14.
How do I use trigonometric functions?
The calculator uses radians by default (as does mathjs). To work in degrees, convert: angle_radians = angle_degrees × π/180. For example, sin(30°) = sin(30 × π/180) = sin(0.5236) ≈ 0.5. To type sin(30°) directly, enter: sin(30 * pi / 180). Common values: sin(0) = 0, cos(0) = 1, tan(45°) = 1, sin(90°) = 1.
What is the difference between log and ln on this calculator?
The "log" button enters log10() which is the common logarithm (base 10). The "ln" button enters log() which is the natural logarithm (base e ≈ 2.71828) in mathjs notation. log10(100) = 2 because 10² = 100. log(e) = ln(e) = 1 because e¹ = e. To compute log in any other base b: log_b(x) = log(x) / log(b).
How do I enter expressions with exponents?
Use the ^ button for exponents. Type 2^10 for 2¹⁰ = 1024. For square root, use sqrt(x). For cube root, use x^(1/3). For x², use the x² button or type x^2. Negative exponents work: 2^(-3) = 0.125. Note: ^ has higher precedence than ×, so 2×3^2 = 2×9 = 18, not 36.