Evaluate math expressions and scientific functions — instantly, with full precision
This tool is for: Students checking homework or exam prep calculations · Engineers and scientists doing quick verification of formulas · Anyone needing trigonometric, logarithmic, or power function results
- The exact result of any mathematical expression with correct order of operations
- Values of scientific functions including sin, cos, tan, log, ln, sqrt, and powers
This selector is the single source of truth for angle units across both the Expression Evaluator and the Function Calculator. Changing it here updates every panel and triggers a warning whenever a trig function is detected in your input.
Formulas Used
Trigonometric Functions
sin(θ), cos(θ), tan(θ) = sin(θ)/cos(θ)
Where: θ = Angle in radians or degrees (radians or degrees)
Source: Standard mathematical functions — Math is Fun reference ✓ Verified
Logarithmic Functions
log₁₀(x), ln(x) = logₑ(x)
Where: x = Input value (must be positive) (dimensionless)
Source: Standard mathematical functions — Khan Academy ✓ Verified
Degree to Radian Conversion
radians = degrees × (π / 180)
Where: degrees = Angle in degrees (degrees), radians = Angle in radians (radians), π = Pi, approximately 3.14159265 (dimensionless)
Source: Standard unit conversion ✓ Verified
Key Insight
The most common source of error in scientific calculations is mixing up degrees and radians. sin(90) in degrees equals 1, but sin(90) in radians equals 0.894 — a completely different value that would produce wrong results downstream. Always verify your angle mode before trusting trig output.
How Changes Affect Your Result
angle_mode: Switching between degrees and radians for the same numeric input rescales trig results by the factor 180/π ≈ 57.296. A value of sin(30) is 0.5 in degrees but -0.988 in radians — a sign change AND magnitude change. Always check angle mode first if a trig answer looks wrong.
Frequently Asked Questions
What is the difference between log and ln on a scientific calculator?
Log (or log₁₀) is the base-10 logarithm, commonly used in chemistry (pH), acoustics (decibels), and earthquake measurement (Richter scale). For example, log(100) = 2 because 10² = 100. Ln is the natural logarithm (base e, where e ≈ 2.71828), used extensively in calculus, physics, and continuous growth models. For example, ln(e) = 1. They are related by the formula: log₁₀(x) = ln(x) / ln(10). Always check which base your textbook or formula expects.
When should I use degrees versus radians for trigonometric functions?
Use degrees when working with everyday angles, geometry problems, navigation, or any context where angles are given in the 0-360 range. Use radians when working with calculus, physics formulas, or any mathematical context that involves pi. Most textbooks in trigonometry and geometry use degrees, while most college-level math and physics courses use radians. The key conversion: 180 degrees = pi radians. If your answer looks wildly wrong, the first thing to check is whether you have the correct angle mode selected.
Why does my calculator show a slightly different result than expected for some expressions?
This is caused by floating-point arithmetic, which is how all modern computers store and calculate decimal numbers. The IEEE 754 standard uses binary representation, which cannot exactly represent all decimal fractions. For example, 0.1 + 0.2 in binary floating point equals 0.30000000000000004, not exactly 0.3. This calculator rounds results to 12 significant digits to minimize visible floating-point artifacts, but tiny rounding differences compared to other calculators are normal and expected. For virtually all practical purposes, the results are accurate.
About This Calculator
Sources:
- MDN Web Docs — JavaScript Math Object — Accuracy and behavior of Math.sin, Math.cos, Math.log, Math.pow and other functions used in the implementation
- Khan Academy — Trigonometry and Logarithms — Mathematical definitions and expected values for standard scientific functions
Limitations:
- Does not support complex numbers — square root of negative numbers returns an error
- Trigonometric functions use radians by default unless degrees mode is explicitly selected
- Very large numbers may lose precision due to IEEE 754 floating-point arithmetic limitations
- Factorial is limited to integers from 0 to 170 due to JavaScript number range
- The expression parser does not support implicit multiplication (e.g., write 2*pi, not 2pi)
When to consult a professional: For calculations involving complex numbers, symbolic algebra, differential equations, or mission-critical engineering, use a dedicated computer algebra system like MATLAB, Mathematica, or Wolfram Alpha.
This scientific calculator uses JavaScript's built-in Math library for function evaluation and a safe expression parser for arbitrary expressions. Results are accurate to approximately 12 significant digits, which is sufficient for virtually all student and engineering quick-check use cases. For mission-critical engineering calculations, verify results with a certified computation tool.