Math Calculators

Math calculators cover the full breadth of mathematical operations, from everyday arithmetic like percentages and fractions, to algebra (quadratic equations, systems of equations), to more advanced topics like logarithms, exponents, and combinatorics. These tools are designed for students at all levels, educators, and anyone who encounters mathematical problems in daily life or professional work.

Mathematics is the language of science, engineering, finance, and computing. Even "everyday" math — calculating percentage changes, splitting numbers into fractions, computing square roots — requires precision that mental arithmetic or rough estimates can't always provide. Our math calculators give exact or high-precision answers along with step-by-step solutions so you can understand the method, not just get the answer.

Percentage calculations appear in nearly every domain of life: sales taxes, discounts, grade scoring, statistical comparisons, financial returns, and survey results. Yet many people find percentage arithmetic counterintuitive — especially percentage increase vs. percentage difference, or compound percentage growth. Our percentage calculator clarifies these concepts with clear formulas and worked examples.

Fractions, decimals, and their interconversions form the backbone of arithmetic. Adding, subtracting, multiplying, and dividing fractions requires finding common denominators and simplifying results — operations that are easy to get wrong under time pressure. Our fraction calculator handles all these operations and shows each step, making it useful both as a tool and as a learning resource.

Percentages express a number as a fraction of 100. "20 percent" means 20 out of every 100, or 0.20 as a decimal. Three fundamental percentage problems appear in practice: (1) What is X% of Y? (2) X is what percent of Y? (3) X is Y% of what number? Each has a straightforward formula, but it's easy to confuse which division goes in which direction.

Percentage change (increase or decrease) compares a new value to an original: Percentage Change = (New − Old) / Old × 100%. A price rising from $40 to $52 is a 30% increase. A price falling from $52 to $40 is a −23.1% decrease — note the asymmetry: these are different percentages because the base (denominator) is different in each case.

Percentage point change is different from percentage change: if an interest rate rises from 3% to 5%, it has risen by 2 percentage points (absolute change) or by 66.7% (relative change). Confusing these two measures is a common source of misunderstanding in media reporting and everyday communication.

Fractions represent division: a/b means a divided by b, where b ≠ 0. Operations on fractions follow specific rules. Addition and subtraction require a common denominator: a/b + c/d = (ad + bc) / bd. Multiplication is straightforward: (a/b) × (c/d) = ac/bd. Division inverts the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.

Simplification (reducing to lowest terms) divides both numerator and denominator by their greatest common divisor (GCD). For example, 12/18 has GCD(12,18) = 6, so 12/18 = 2/3. Mixed numbers like 2¾ combine a whole number with a proper fraction; they convert to improper fractions as (2 × 4 + 3) / 4 = 11/4 for calculation purposes.

Exponentiation (raising a base to a power) and logarithms (the inverse operation) are fundamental to science, finance, and computing. 2¹⁰ = 1,024; log₂(1024) = 10. The natural logarithm (base e, where e ≈ 2.71828) and common logarithm (base 10) appear throughout science and engineering.

Key exponent rules: aᵐ × aⁿ = a^(m+n); aᵐ / aⁿ = a^(m−n); (aᵐ)ⁿ = a^(mn); a⁰ = 1 (for a ≠ 0); a^(−n) = 1/aⁿ; a^(1/n) = ⁿ√a (the nth root). These rules are essential for simplifying expressions and solving exponential equations.

Logarithms convert multiplication to addition and exponentiation to multiplication — the properties that made logarithm tables so valuable for calculation before computers. Today, logarithms are used in information theory (bits = log₂ of possibilities), decibel scales, pH calculations, Richter scale magnitudes, musical intervals, and compound growth problems.

Algebra deals with mathematical expressions containing variables — letters representing unknown or variable quantities. Solving an equation means finding the value(s) of the variable that make the equation true. Linear equations (degree 1) have one solution; quadratic equations (degree 2) have zero, one, or two real solutions; polynomial equations of degree n have at most n real solutions.

The quadratic formula solves any equation of the form ax² + bx + c = 0: x = [−b ± √(b² − 4ac)] / 2a. The discriminant b² − 4ac determines the nature of the solutions: if positive, two distinct real solutions; if zero, one repeated real solution; if negative, two complex (no real) solutions.

Systems of linear equations — two or more equations with two or more variables — can be solved by substitution, elimination, or matrix methods (Gaussian elimination, Cramer's rule). Our algebra calculators show the full solution process for each method.