Math Calculator
Perform arithmetic, algebra, trigonometry, logarithms, and statistical calculations with our free online math calculator. Get instant results with step-by-step breakdowns for complex expressions.
What Is a Math Calculator?
A math calculator is a free online tool that performs a wide range of mathematical operations, from basic arithmetic to advanced functions like trigonometry, logarithms, and statistics. It's designed for students, teachers, professionals, and anyone who needs quick, accurate mathematical results.
Our calculator supports multiple operation types: basic arithmetic (addition, subtraction, multiplication, division), powers and roots, trigonometric functions, logarithms, statistical analysis, and linear equation solving.
How Does the Math Calculator Work?
The calculator uses JavaScript's built-in Math library and custom algorithms to perform calculations:
Basic Arithmetic: num1 <operator> num2
Power/Root: baseexponent or exponent√base
Trigonometry: sin(angle), cos(angle), tan(angle), etc.
Logarithm: logbase(value) or ln(value)
Statistics: Mean, median, mode, range, variance, standard deviation
Equation Solver: Linear equations in the form ax + b = c
Results are displayed with your chosen precision.
Why Use This Math Calculator?
- Versatile: Covers arithmetic, algebra, trigonometry, logarithms, and statistics.
- Free & Easy: No registration, no fees, just enter your numbers and get results.
- Step-by-Step: See the breakdown of calculations for complex operations.
- Visual: Charts and graphs for statistical and trigonometric data.
- Mobile-Friendly: Works on any device, from desktop to smartphone.
Common Mathematical Operations
- Arithmetic: Addition, subtraction, multiplication, division, modulo
- Powers & Roots: Square, cube, nth power, square root, cube root, nth root
- Trigonometry: Sine, cosine, tangent, cotangent, secant, cosecant
- Logarithms: Base 10, natural log (ln), base 2
- Statistics: Mean, median, mode, range, variance, standard deviation
- Equation Solving: Linear equations with one variable
❓ Math Calculator FAQ
What is the difference between arithmetic and algebra?
Arithmetic deals with basic operations on numbers (addition, subtraction, multiplication, division). Algebra introduces variables (like x or y) that represent unknown values, allowing you to solve equations and work with expressions symbolically.
How do I calculate percentages with this calculator?
For percentage calculations, use the basic arithmetic mode. For example, to find 20% of 150, multiply 150 × 0.20. Or use the formula: (part ÷ whole) × 100. For quick percentage calculations, try our Percentage Calculator.
What is the order of operations (PEMDAS)?
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This is the standard order for evaluating mathematical expressions.
How do I calculate the square root of a number?
Select the "Power / Root" operation type, then choose "Square Root" from the Power Type dropdown. Enter your number and click Calculate.
What is the difference between mean, median, and mode?
Mean is the average of all numbers (sum ÷ count). Median is the middle value when numbers are sorted. Mode is the most frequently occurring value. Use the Statistics mode to calculate all three at once.
How do I calculate the standard deviation?
Select the "Statistics" operation type, enter your data set as comma-separated values, and choose "Standard Deviation" from the statistic dropdown. The calculator uses the population standard deviation formula.
What is a logarithm and how do I use it?
A logarithm answers the question: "What exponent do I need to raise the base to get this value?" For example, log₁₀(100) = 2 because 10² = 100. Use the Logarithm mode with your chosen base.
How do I solve equations with this calculator?
Select the "Equation Solver" operation type and enter a linear equation like "3x + 5 = 20". The calculator will solve for x and show the step-by-step solution.
What is the difference between degrees and radians?
Degrees and radians are two units for measuring angles. 180° = π radians. Trigonometry functions can be calculated in either unit. Select your preferred unit in the advanced options.
How do I calculate trigonometric functions?
Select the "Trigonometry" operation type, enter your angle, and choose the function (sin, cos, tan, etc.). Make sure your angle unit (degrees or radians) is set correctly in the advanced options.
What is the difference between variance and standard deviation?
Variance is the average of the squared differences from the mean. Standard deviation is the square root of variance, giving a measure of spread in the same units as the original data. Standard deviation is more commonly used.
Can I calculate fractions with this calculator?
Yes. Enter fractions as decimals (e.g., 0.75 for ¾) or use division (e.g., 3/4). For more advanced fraction operations, try our Fraction Calculator.
What is the modulo operation?
Modulo (or modulus) gives the remainder after division. For example, 10 mod 3 = 1 because 10 ÷ 3 = 3 remainder 1. It's useful in programming, cryptography, and number theory.
How do I calculate the range of a data set?
Range is the difference between the maximum and minimum values in a data set. Use the Statistics mode and select "Range" as the statistic to calculate it automatically.
What is the difference between population and sample standard deviation?
Population standard deviation uses all data points (divides by n). Sample standard deviation uses a sample (divides by n-1) to estimate the population parameter. This calculator uses the population formula.
How do I calculate the nth root of a number?
Select the "Power / Root" operation type, enter the base number, the root index (e.g., 3 for cube root), and choose "Root" from the Power Type dropdown.
What is the difference between natural log and common log?
Natural log (ln) uses base e (≈2.71828). Common log (log₁₀) uses base 10. Natural log is commonly used in calculus and natural sciences, while common log is used in chemistry and engineering.
How accurate is this calculator?
This calculator uses JavaScript's double-precision floating-point arithmetic, which is accurate to about 15-16 significant digits. Results are rounded to your selected precision for display.