Math Calculators: The Complete Guide to Percentages, Fractions, Statistics & More
Every everyday and academic math calculation — from percentage shortcuts to quadratic equations — explained with clear formulas, step-by-step examples, and free calculators.
Free Math Calculators
The 14 Math Tools — What Each One Solves
| Calculator | Solves | Common Use |
|---|---|---|
| Percentage | 6 types of % problems | Tips, discounts, growth rates, tax |
| Fraction | Add, subtract, multiply, divide | Cooking, construction, finance |
| Ratio | Simplify, scale, proportion | Recipes, maps, aspect ratios |
| Statistics | Mean, median, mode, SD | Data analysis, surveys, grades |
| Grade & GPA | Weighted average, GPA | Course grades, academic planning |
| Tip | Tip amount, bill split | Restaurants, service workers |
| Discount | Percent off, original price | Shopping, pricing, sales |
| % Increase | Change %, CAGR | Revenue growth, stock returns |
| Date | Days between, add/subtract | Project timelines, age, deadlines |
| Equation Solver | Linear equations | Break-even, algebra homework |
| Quadratic Solver | ax²+bx+c=0 | Physics, profit maximisation |
| Pythagorean | Right triangle sides | Construction, geometry |
| Scientific Notation | Powers of 10 | Physics, astronomy, chemistry |
Percentages — The Most Used Math Skill
Percentages appear in every financial, business, and everyday context. There are 6 types of percentage problems — and a different formula for each one.
What is X% of Y? → Y × (X ÷ 100)
X is what % of Y? → (X ÷ Y) × 100
X is Y% of what? → X ÷ (Y ÷ 100)
% increase X to Y → ((Y − X) ÷ X) × 100
% decrease X to Y → ((X − Y) ÷ X) × 100
Reverse: Y after X% off → Y ÷ (1 − X ÷ 100)
→ Use the Percentage Calculator · Read the full guide
Fractions — Step by Step
Adding fractions requires a common denominator. Multiplying doesn't. Dividing flips the second fraction and multiplies.
Add/Subtract: find LCD → convert → operate on numerators
Multiply: a/b × c/d = (a×c) / (b×d)
Divide: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
→ Use the Fraction Calculator · Read the full guide
Statistics — Summarising Data
The four most important descriptive statistics are mean (average), median (middle value), mode (most common), and standard deviation (spread from the mean). Use median instead of mean when your data has extreme outliers — a single $1M salary in a group of $50K earners will pull the mean far from the typical value.
→ Use the Statistics Calculator · Read the full guide
Grade & GPA Calculation
GPA = sum of (grade points × credit hours) ÷ total credit hours. A in a 3-credit course = 4.0 × 3 = 12 grade points. Weighted GPA allows AP/honours courses to use a 5.0 scale.
All Math Guides
Frequently Asked Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage, then divide by 100. For 15% of 200: 200 × 15 ÷ 100 = 30. Or use the shortcut: move the decimal one place left (10% of 200 = 20), then adjust. Our percentage calculator handles all 6 types of percentage problems.
How do I add fractions with different denominators?
Find the Least Common Denominator (LCD) — the smallest number both denominators divide into. Convert each fraction to that denominator, then add the numerators. Example: 1/3 + 1/4 → LCD is 12 → 4/12 + 3/12 = 7/12.
What is the difference between mean, median, and mode?
Mean = sum ÷ count (the average). Median = the middle value when sorted (better for skewed data). Mode = the most frequent value. For the dataset {2, 3, 3, 7, 10}: mean = 5, median = 3, mode = 3. Use median when your data has extreme outliers.
How do I calculate GPA on a 4.0 scale?
Convert each grade to grade points (A=4, B=3, C=2, D=1, F=0), multiply by credit hours, sum all the results, then divide by total credit hours. Weighted GPA (for AP/honours classes) uses higher grade point values (A=5) for the harder classes.
How do I calculate percentage increase?
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If revenue went from $80,000 to $100,000: (100,000 − 80,000) ÷ 80,000 × 100 = 25% increase. For compound annual growth (CAGR): ((End ÷ Start)^(1/years) − 1) × 100.
What is the tip etiquette in the US?
Sit-down restaurants: 15–20% for good service, 20–25% for excellent. Counter service / fast casual: 10–15% optional. Delivery: 15–20% of the order total. Hair / beauty: 15–20%. Always tip on the pre-tax total. In most other countries, tipping is smaller or not customary.