Basic Math Calculators
Free percentage, average, fraction, square root, and ratio calculators. Fast, accurate basic math tools for students and professionals.
Basic Math Calculators - Arithmetic Done Right, Every Time
Basic math calculations underpin almost every professional and academic task. Discounts, percentages, averages, ratios, fractions - these appear constantly in finance, science, engineering, cooking, and everyday decision-making. These calculators eliminate arithmetic errors and, more importantly, show the formula so you understand the method.
Five Basic Math Calculators
Percentage Calculator - Three modes: (1) what is X% of Y? (2) X is what percent of Y? (3) percentage change from X to Y. The most versatile math calculator on the site - used for discount calculations, exam marks, profit/loss percentages, and population growth rates.
Average Calculator - Arithmetic mean, median, and mode for any set of comma-separated numbers, plus count, sum, min, and max. Handles any dataset size.
Fraction Calculator - Add, subtract, multiply, and divide fractions with unlike denominators. Shows full working: LCM for denominator, equivalent fractions, operation, and simplification. Supports mixed numbers and improper fractions.
Square Root Calculator - √x and nth roots, plus x² and xⁿ. Flags perfect squares explicitly. Used in geometry (Pythagorean theorem, see the Pythagorean Calculator), physics, and algebra.
Ratio Calculator - Three modes: (1) simplify a ratio to lowest terms (e.g., 15:25 → 3:5), (2) find a missing value in a proportion (cross-multiplication), (3) scale a ratio to a target total (e.g., mix 3:5:2 totalling 500g). Used in recipe scaling, map reading, and financial ratio analysis.
When Basic Math Gets Tricky
The most common error in percentage calculations is confusing percentage points and percentages - if interest rates rise from 4% to 6%, that is a 2 percentage-point increase but a 50% increase in rate. The Percentage Calculator handles both interpretations correctly.
For data analysis, the Average Calculator shows mean, median, and mode simultaneously - relevant because for skewed data (like income), median is a more representative typical value than mean. For deeper statistics, see the Standard Deviation Calculator.
Frequently Asked Questions
What is the formula for percentage change?
Percentage change = ((New − Old) ÷ Old) × 100. Positive = increase, negative = decrease. For example: sales from ₹80,000 to ₹100,000 = ((100,000 − 80,000) ÷ 80,000) × 100 = 25% increase. Try it in the Percentage Calculator.
What is the difference between mean, median, and mode?
Mean is the arithmetic average. Median is the middle value when sorted - unaffected by outliers. Mode is the most frequent value. The Average Calculator returns all three, plus range and sum, for any dataset.
How does the fraction calculator simplify results?
The Fraction Calculator divides both numerator and denominator by their GCD (found via the Euclidean algorithm). For example, 6/8 simplifies by GCD(6,8) = 2, giving 3/4.
How do I find a missing value in a proportion?
In the Ratio Calculator, use the "Find Missing Value" mode. For 3:5 = ?:20, it uses cross-multiplication: ? = (3 × 20) ÷ 5 = 12.