Math Calculators
From simple percentages to algebra and geometry — our free math calculators show you the answer and the working. Built for students, teachers, and anyone who wants to check their calculations.
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Percentage calculations, ratios, fractions, and basic arithmetic
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Math Glossary — Key Terms Explained
- Percentage
- A number expressed as a fraction of 100. To find X% of Y: multiply Y by X/100. To find what percentage X is of Y: divide X by Y and multiply by 100.
- Mean (Average)
- The sum of all values divided by the count. The most common measure of central tendency. Sensitive to outliers — a single extreme value significantly affects the mean.
- Median
- The middle value when all values are arranged in order. Less affected by outliers than the mean. For an even number of values, median = average of two middle values.
- Mode
- The most frequently occurring value in a dataset. A dataset can have no mode (all values unique) or multiple modes (bimodal, trimodal, etc.).
- Exponent
- A number indicating how many times the base is multiplied by itself. 2^3 = 2 × 2 × 2 = 8. Any number to the power of 0 = 1. Any number to the power of 1 = itself.
Frequently Asked Questions
How do I calculate a percentage increase?
Percentage increase = (New Value − Old Value) ÷ Old Value × 100. Example: price rises from £80 to £100: (100 − 80) ÷ 80 × 100 = 25% increase. For a decrease, the formula is the same — the result will be negative.
What is the difference between mean, median, and mode?
Mean: sum ÷ count. Median: middle value. Mode: most frequent value. For a symmetric distribution, all three are equal. For skewed data (e.g., incomes), the median is more representative — a few very high incomes pull the mean up, making the median a better measure of 'typical' income.
How do I add fractions with different denominators?
Find the least common denominator (LCD), convert both fractions to that denominator, then add the numerators. Example: 1/3 + 1/4: LCD = 12; 1/3 = 4/12; 1/4 = 3/12; sum = 7/12.
What is the area of a circle?
Area = π × r², where r is the radius (half the diameter). If the diameter is 10 cm, r = 5 cm, area = π × 25 = 78.54 cm². Circumference = 2 × π × r = 31.42 cm.