Math Calculators
Fractions, ratios, averages and the rest of school-and-spreadsheet arithmetic — each one showing the working, not just the answer.
25 free calculators · updated August 2026
Several of these tools answer questions that sound interchangeable but are not. Mean, Median, Mode and Range Calculator gives three centers and the gap between the extremes, because which one is useful depends on the data; Standard Deviation and Variance Calculator requires a sample or population choice because that changes the divisor. Percentage Difference Calculator separates difference, change, and error by their reference value. Geometry is input driven: Circle Calculator can recover related measurements from a known measurement, while Triangle Calculator selects among side and angle cases and can expose an ambiguous result. The input labels are part of the mathematics, not mere form fields.
Fraction and Mixed Number Calculator
Add, subtract, multiply and divide fractions — exactly, with the answer as a mixed number and the reducing step shown.
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Decimal to Fraction Calculator
Convert a decimal to a fraction in lowest terms, reading the digits exactly rather than guessing a near one.
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Fraction to Decimal Calculator
Convert a fraction to a decimal by long division, with the repeating block marked and measured.
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Percentage Difference Calculator
Percentage difference, change and error side by side — because they are three different answers.
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Ratio Calculator
Simplify a ratio to lowest terms and split a total by it — two terms or three.
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Proportion Calculator
Solve a/b = c/d for any missing term, with both cross products shown.
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Standard Deviation and Variance Calculator
Standard deviation, variance and the coefficient of variation from one list — sample or population, the switch that changes all three.
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Mean, Median, Mode and Range Calculator
Mean, median and mode together — because all three are called the average — plus the range they say nothing about.
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Significant Figures Calculator
Count the significant figures in a number and round to any number of them, with the ambiguous cases flagged.
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GCF Calculator
Greatest common factor — also called the greatest common denominator, GCD or HCF — with every prime factorisation shown.
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Prime Factorization Calculator
Break a single number into its prime factors, with the exponent form, every divisor, and how many there are.
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LCM Calculator
Least common multiple of any set of whole numbers, showing where their multiples first meet.
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Slope Calculator
Two points in, the whole line out — slope, equation, both intercepts and the angle of inclination.
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Distance Formula Calculator
The distance between two points in exact radical form, with every step of the substitution shown — in 2D or 3D.
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Quadratic Formula Calculator
Roots, discriminant and vertex — including the complex roots most calculators refuse.
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Square Root Calculator
The decimal, and the simplified radical form a phone will not give you.
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Exponent Calculator
Raise a number to any power, including the negative exponents that give reciprocals and the fractional ones that give roots.
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Long Division Calculator
Quotient, remainder and the written working, one digit at a time.
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Circle Calculator
Radius, diameter, circumference or area — enter any one and get the other three, with both circumference formulas shown.
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Rectangle Calculator
Area, perimeter and diagonal — or a missing side from any one of them.
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Trapezoid Calculator
Area from the parallel sides and height, or the height from all four sides.
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Triangle Calculator
SSS, SAS, ASA, AAS and the ambiguous SSA case — and it names the triangle isosceles, equilateral or right.
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Cylinder Volume and Surface Area Calculator
Volume in litres and gallons, curved wall and total surface area — or the radius a tank of known capacity needs.
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Cone Volume and Surface Area Calculator
Curved and total surface area, and exactly one third of its cylinder — with the slant height kept separate from the height.
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Sphere Surface Area and Volume Calculator
Surface area and volume from any one of four measurements, each direction a closed form.
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Guides for these tools
Long-form answers behind 9 of the calculators above.
- Why the Quadratic Formula Loses Accuracy on One of Its Two RootsCompleting the square takes four lines and produces the formula. It also shows which of the two roots is safe to trust, and the calculator on this site was corrected to use the other route.
- Geometry Backwards: Finding the Radius from the AreaEvery geometry formula is printed in the direction you need least. Running it backwards is not the same operation reversed; it is a root, and roots can refuse.
- When Cross Multiplication Gives You the Wrong AnswerCross multiplication answers every question you put to it, including the ones it should refuse. The test is one line: if the input were zero, would the output be zero?
- How to Add Fractions With Different Denominators — and Why the Rule Works1/2 + 1/3 done the wrong way gives 2/5 — smaller than the 1/2 you started with. A sum must beat both addends, and that check is free.
- Percent Grade to Degrees: Why a 100% Grade Is 45 Degrees, Not VerticalA 100% grade is 45 degrees. Percent grade has no ceiling; degrees stop below 90, and that mismatch is where every conversion error starts.
- Scale Factor: Why Doubling the Size Gives Four Times the AreaTwice as big means four times the paint and eight times the water. Lengths take k, areas take k², volumes take k³, and every scaling error is the wrong exponent.
- Percentage Difference vs Percentage Change: Which One Do You Want?40 and 60 are 40% apart, 50% more, and 33.3% less. All three are correct. The denominator is the decision.
- How to Find the Volume of Hollow, Partial, and Composite SolidsA decomposition-first guide to pipes, frustums, domes, and partly filled tanks, with formulas and checks for avoiding geometric and unit errors.
- How to Compare Two Data Sets: Center, Spread, and Relative DifferenceA practical workflow for deciding whether two sets are comparable, describing their typical values and variation, and reporting differences without overstating them.