Free Math Calculators Online
Six free math calculators covering the calculations people need most — percentages, averages, ratios, scientific functions, unit conversion and basic arithmetic. Every tool shows the formula used and the step-by-step working alongside the answer. No sign-up, no cost, no usage limits.
All Math Calculators
Choose the calculator that matches your task. If you are not sure which one to use, the guide below maps common problems to the right tool.
- Percentage Calculator — Find a percentage of a number, calculate percentage change, or work out what percentage one number is of another. Three calculation modes in one tool.
- Average Calculator — Calculate mean, median, mode and range from any list of numbers. Paste a comma-separated list and get all four measures at once.
- Ratio and Proportion Calculator — Simplify ratios, solve for a missing value in a proportion, and find equivalent ratios. Covers cooking, finance, maps and scale problems.
- Scientific Calculator — Trigonometric functions (sin, cos, tan), logarithms (log, ln), exponents, square roots and factorials. Keyboard-friendly, fast-loading.
- Unit Conversion Calculator — Convert between units of length, weight, temperature, volume, area and speed. Covers both metric and imperial, including common cooking and travel conversions.
- Simple Calculator — Fast, clean arithmetic. Add, subtract, multiply, divide. No clutter, no ads inside the tool.
Which Math Calculator Should You Use?
The table below maps the most common calculation tasks to the right tool. If your problem appears in the left column, click the tool name to go directly to that calculator.
| Your task | Calculator to use | Example |
|---|---|---|
| Find X% of a number | Percentage Calculator | What is 18% of 450? |
| Calculate percentage increase or decrease | Percentage Calculator | Price went from £80 to £100 — what is the % increase? |
| Calculate a discount | Percentage Calculator | 30% off £120 — what is the final price? |
| Find the mean, median or mode | Average Calculator | Average of 12, 17, 9, 25, 31 |
| Simplify a ratio | Ratio Calculator | Simplify 24:36 |
| Solve a proportion — find a missing value | Ratio Calculator | A:B = 3:5 and A = 90 — find B |
| Trigonometry (sin, cos, tan) | Scientific Calculator | sin(45°) or cos(1.2 radians) |
| Logarithms or exponents | Scientific Calculator | log₁₀(500) or ln(e³) |
| Convert cm to inches, kg to lbs | Unit Converter | 175 cm in feet and inches |
| Convert temperature | Unit Converter | 37°C in Fahrenheit |
| Basic arithmetic — add, subtract, multiply, divide | Simple Calculator | Any everyday calculation |
Percentage Calculator — Three Types of Percentage Problem
Percentage calculations appear in almost every domain: shopping discounts, tax calculations, exam scores, salary raises, investment returns and data analysis. The difficulty is that "percentage" covers three distinct calculation types, each with a different formula.
Type 1 — Finding a percentage of a number
Formula: (Percentage ÷ 100) × Number
Example: What is 15% of 240? → (15 ÷ 100) × 240 = 36
When to use: Calculating a tip, working out VAT, finding a discount amount.
Type 2 — Finding what percentage one number is of another
Formula: (Part ÷ Whole) × 100
Example: 18 is what percent of 72? → (18 ÷ 72) × 100 = 25%
When to use: Test scores ("I got 54 out of 80"), attendance rates, market share, budget percentages.
Type 3 — Percentage change (increase or decrease)
Formula: ((New − Old) ÷ Old) × 100
Example: Price rises from £80 to £100 → ((100 − 80) ÷ 80) × 100 = 25% increase
When to use: Year-on-year growth, price comparison, salary increase, weight loss tracking.
The Percentage Calculator handles all three types in one place. Select the mode that matches your problem, enter the numbers, and the result appears with the formula and working shown.
Average Calculator — Mean, Median and Mode Explained
"Average" is not a single calculation — it refers to three different measures of central tendency, each suited to a different type of data.
Mean (arithmetic average)
Add all values and divide by the count. The mean is the most commonly used average but can be distorted by extreme outliers. A dataset of 10, 12, 11, 13, 150 has a mean of 39.2, which does not represent the typical value. In these cases, use the median instead.
Median (middle value)
Sort the values in order and find the middle one. If there is an even number of values, the median is the mean of the two middle values. The median is more useful than the mean for skewed data — income, house prices, and test scores with outliers are all better described by their median.
Mode (most frequent value)
The value that appears most often. Mode is most useful for categorical or discrete data — the most common shoe size in a shop, the most frequent rating in a survey, or the most common score on a test. A dataset can have more than one mode if two values appear equally often.
Range
The difference between the largest and smallest values. Range gives a quick measure of spread — how widely the data varies. It is sensitive to outliers because it only uses the two extreme values.
The Average Calculator computes mean, median, mode and range from any list of numbers simultaneously. Paste your numbers in as a comma-separated list and all four values are returned at once.
Ratio and Proportion Calculator — Simplify, Scale and Solve
Ratios compare two quantities. Proportions state that two ratios are equal. Both appear across a wide range of everyday problems.
Where ratios appear in practice
- Cooking: scaling a recipe from 4 portions to 10 portions
- Finance: a debt-to-equity ratio of 1.4:1
- Maps and scale drawings: a 1:50,000 scale map
- Photography and screens: aspect ratios such as 16:9 or 4:3
- Chemistry: mixing solutions in a 2:5 ratio by volume
- Construction: concrete mix ratios such as 1:2:3 (cement:sand:aggregate)
How to simplify a ratio
Find the Greatest Common Divisor (GCD) of both numbers and divide each by it. To simplify 36:48, the GCD is 12. Dividing both gives 3:4.
How to solve a proportion
If A:B = C:D, then A × D = B × C (cross-multiplication). To find the missing value: if 3:5 = ?:20, then ? = (3 × 20) ÷ 5 = 12.
The Ratio and Proportion Calculator handles simplification, scaling and missing-value problems automatically.
Scientific Calculator Online — Trig, Logarithms and More
A scientific calculator is needed for any calculation that goes beyond basic arithmetic. The most common use cases are:
Trigonometric functions
Sin, cos and tan — and their inverses arcsin, arccos, arctan — are used in physics, navigation, architecture and any problem involving angles and triangles. The calculator supports both degrees and radians.
Logarithms
Log base 10 (log₁₀) appears in pH calculations, decibel measurements and Richter scale readings. Natural log (ln) is used in exponential growth and decay problems, compound interest formulas and statistics.
Exponents and roots
Squaring, cubing and raising to any power, plus square roots and nth roots. Used in geometry (area and volume), physics and financial compound growth.
Factorials
Factorials (n!) appear in combinatorics and probability — calculating how many ways items can be arranged or selected.
The Scientific Calculator on this site uses 64-bit double-precision floating-point arithmetic — the same standard as Excel and most engineering software. It is keyboard-friendly and works on mobile without zooming.
Unit Conversion Calculator — Metric, Imperial and More
Unit conversion is one of the most searched calculation types because it spans every area of life — travel, cooking, health, shopping and science all involve units from different systems.
Length
Millimetres, centimetres, metres, kilometres, inches, feet, yards, miles. Common conversions: cm to inches, metres to feet, km to miles.
Weight and mass
Milligrams, grams, kilograms, metric tonnes, ounces, pounds, stone. Common conversions: kg to lbs, stone to kg, grams to ounces.
Temperature
Celsius, Fahrenheit and Kelvin. Common conversions: °C to °F for international recipes and weather, Kelvin for science.
Volume
Millilitres, litres, fluid ounces, cups, pints, quarts, gallons. Common conversions: ml to cups, litres to gallons, fl oz to ml.
Area
Square centimetres, square metres, square kilometres, square inches, square feet, acres, hectares. Common conversions: sq ft to sq m, acres to hectares.
Speed
Metres per second, kilometres per hour, miles per hour, knots. Common conversions: mph to km/h, m/s to km/h.
The Unit Conversion Calculator covers all six categories above. Select the unit type, choose your input and output units, enter the value, and the conversion result appears instantly with the conversion factor shown.
How to Use These Math Calculators
Every tool on this site follows the same three-step flow:
- Choose your calculator — use the list above or the comparison table to find the tool that matches your problem.
- Enter your values — all input fields are labelled in plain language. Required fields are marked. If a field is unclear, a short note below the label explains it.
- Read the result and working — the answer appears instantly. Below it, the formula used and the step-by-step calculation are shown so you can verify the result and understand how it was reached.
No account is needed. No data is stored. All calculations happen in your browser — nothing is sent to any server.
Frequently Asked Questions
What is the best free online math calculator?
The best free math calculator depends on what you need to solve. For percentages, discounts and percentage change, use the Percentage Calculator. For mean, median and mode, use the Average Calculator. For trigonometry, logarithms and exponents, use the Scientific Calculator. For converting between units like cm to inches or kg to lbs, use the Unit Conversion Calculator. Every tool on this site shows the formula and working — not just the answer.
How do I calculate percentage increase?
The formula for percentage increase is: ((New Value − Old Value) ÷ Old Value) × 100. For example, if a price rises from £80 to £100: (100 − 80) ÷ 80 × 100 = 25%. Use the Percentage Calculator and select the percentage change mode for an instant result with the working shown.
What is the difference between mean, median and mode?
Mean is the arithmetic average — add all values and divide by the count. It works best for data without extreme outliers. Median is the middle value when your numbers are sorted in order. It is more accurate than the mean for skewed data such as income or house prices. Mode is the most frequently occurring value in a dataset, most useful for categorical data such as the most common test score or most popular product size. The Average Calculator computes all three at once.
How do I simplify a ratio?
Find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, to simplify 24:36 — the GCD is 12. Dividing both by 12 gives 2:3. The Ratio and Proportion Calculator simplifies any ratio automatically and also solves for missing values in a proportion.
Can I use these math calculators on my phone?
Yes. Every math calculator on this site is mobile-responsive and works on all screen sizes without needing to zoom, scroll sideways or download an app. No sign-up or account is required.
Do these calculators show the working or just the answer?
Every calculator on this site shows the formula used and the step-by-step working alongside the result. This means you can verify the answer yourself, understand how it was reached, and apply the same method to similar problems.
What units does the unit conversion calculator support?
The Unit Conversion Calculator covers length (mm, cm, m, km, inches, feet, yards, miles), weight (mg, g, kg, oz, lbs, stone), temperature (Celsius, Fahrenheit, Kelvin), volume (ml, litres, fl oz, cups, pints, gallons), area (cm², m², sq ft, acres, hectares) and speed (m/s, km/h, mph, knots).
How accurate are the math calculators on this site?
All calculators use standard, verified formulas. The Scientific Calculator uses 64-bit double-precision floating-point arithmetic, the same standard used in Excel and most engineering software. For everyday calculations involving percentages, averages and ratios, results are accurate to the inputs provided. Where a formula involves estimation or rounding, this is stated on the tool page.
Other Calculator Categories
These tools are live across the rest of the site — each category uses the same format: instant results, formula shown, plain-language explanations.
- Finance Calculators — Loan EMI, mortgage repayment, compound interest, savings growth and tip calculator.
- Health Calculators — BMI, daily calorie target (TDEE), water intake, body fat percentage and age calculator.
- Fitness Calculators — Calories burned, running pace, macro calculator and one-rep max.
- Everyday Calculators — Date difference, sleep cycle, fuel cost and time calculator.