Free Learning Tools
Free Maths Calculators
Every calculator here shows the method, not just the answer: the steps are written out the way a tutor would set them out on paper. Built by SHLC's maths tutors for 11+ and GCSE families.
Percentages
Percentage Calculator
Work out a percentage of any number, with the decimal method shown step by step.
Percentage Change Calculator
Find the percentage increase or decrease between two values, divided by the original.
Reverse Percentage Calculator
Work backwards from a value after a percentage change to the original amount.
What Percentage Calculator
Find what percentage one number is of another, the classic test score question.
Simple Interest Calculator
Interest that stays the same every year: one year, the total, and the final balance.
Percentage Increase and Decrease Calculator
Increase or decrease any amount by a percentage, with the multiplier shown.
VAT Calculator
Add VAT to a price or take it back out, without the classic removal mistake.
Growth and Decay Calculator
Repeated percentage change: appreciation, depreciation and populations.
Profit and Loss Calculator
Profit or loss in pounds and as a percentage of what you paid.
Fractions and Decimals
Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, with full working.
Fraction to Decimal Calculator
Switch between fractions, decimals and percentages, in any direction, with steps.
Rounding Calculator
Nearest 10, 100 and 1,000, decimal places and significant figures, with the decider digit named.
Fraction of an Amount Calculator
Divide by the bottom, multiply by the top, forwards or in reverse.
Ordering Numbers Calculator
Mixed fractions, decimals and percentages put in order, conversions shown.
Recurring Decimals Calculator
Any recurring decimal turned into an exact fraction, algebra proof included.
Adding Fractions Calculator
Add two fractions or mixed numbers, with the common denominator found for you.
Subtracting Fractions Calculator
Take one fraction from another, negative answers and mixed numbers included.
Multiplying Fractions Calculator
Multiply straight across, no common denominator needed, then simplify.
Dividing Fractions Calculator
Keep, flip, change: dividing turned into multiplying, step by step.
Simplify Fractions Calculator
Reduce any fraction to its simplest form, with the highest common factor named.
Equivalent Fractions Calculator
List fractions worth the same, or fill in the missing number in a pair.
Number
HCF and LCM Calculator
Highest common factor and lowest common multiple of two or three numbers, with a Venn diagram.
Prime Factor Calculator
Any number as a product of prime factors, shown as a division ladder and in index form.
Standard Form Calculator
Convert between ordinary numbers and standard form, counting the point moves.
Powers and Roots Calculator
Powers as repeated multiplication, square and cube roots, and simplified surds.
Estimation Calculator
Round every number to 1 significant figure, then estimate like the exam wants.
Bounds Calculator
Upper bound, lower bound and the error interval for any rounded value.
Indices Calculator
The laws of indices with the law named: add, subtract or multiply the powers.
Surds Calculator
Simplify, multiply and rationalise surds, everything kept exact.
Written Methods Calculator
Long multiplication and bus stop division, narrated digit by digit.
Negative Numbers Calculator
Add, subtract, multiply and divide negatives, with the sign rule named.
Factors of a Number Calculator
Every factor of a number, found in pairs so none go missing.
Roman Numerals Converter
Numbers into Roman numerals and back, with the subtraction pairs explained.
Ratio and Proportion
Ratio Calculator
Simplify two and three part ratios, with the highest common factor named.
Ratio Sharing Calculator
Share an amount in a ratio, or find a missing value in equivalent ratios.
Scale Calculator
Map and model scales: map to real, real to map, or find the scale itself.
Unit Converter
Length, mass, capacity, area, volume and time, with the unit link stated first.
Best Buy Calculator
Two pack sizes, one fair comparison: price per unit, winner named.
Exchange Rate Calculator
Convert money between currencies from any rate, both directions explained.
Direct and Inverse Proportion Calculator
Find the constant k first, write the formula, then use it. Every time.
Shape
Area and Perimeter Calculator
Rectangles, triangles, circles, trapezia and parallelograms, formula first.
Volume and Surface Area Calculator
Cuboids, cylinders, spheres, cones and prisms, in cubed and squared units.
Circle Calculator
Start from any circle measurement and get radius, diameter, circumference and area.
Angles Calculator
Polygon angles, missing triangle angles, angles on a line and around a point.
Pythagoras Calculator
The missing side of a right-angled triangle, with squares and surds shown.
Trigonometry Calculator
SOHCAHTOA: the right ratio picked for you, for missing sides and angles.
Sector and Arc Calculator
Arc length and sector area as a fraction of the circle, exact in pi.
Similar Shapes Calculator
One scale factor, three powers: lengths, areas and volumes scaled correctly.
Sine and Cosine Rule Calculator
Sides and angles in triangles without a right angle, rule chosen for you.
Algebra and Graphs
Quadratic Equation Calculator
The quadratic formula with the discriminant checked first, surds kept exact.
Simultaneous Equations Calculator
Two equations solved by elimination, every line of algebra shown.
Straight Line Graph Calculator
Two points in, everything out: gradient, midpoint, length and y = mx + c.
Nth Term Calculator
The nth term of linear and quadratic sequences, built from the differences.
Solving Equations Calculator
One step, two step, brackets, fractions and x on both sides, solved by the balance method.
Inequalities Calculator
Solve linear inequalities, with the sign flip for negatives built in.
Expanding Brackets Calculator
Single and double brackets expanded with the FOIL products written out.
Factorising Calculator
Common factors pulled out and quadratics split into double brackets.
Completing the Square Calculator
Rewrite a quadratic as a squared bracket, and read off the turning point.
Substitution Calculator
Put numbers into an expression, with brackets kept round the negatives.
Changing the Subject Calculator
Rearrange a formula to make x the subject, even when x appears twice.
Simplifying Expressions Calculator
Collect like terms, keeping the x, the y and the numbers in their own groups.
Parallel and Perpendicular Lines Calculator
Find the line through a point that is parallel or perpendicular to another.
Geometric Sequences Calculator
Sequences that multiply, with the common ratio and the nth term rule.
Cubic Equation Calculator
Solve ax³ + bx² + cx + d = 0 with the factor theorem, then the quadratic that is left.
Three Unknowns Simultaneous Equations Calculator
Three equations in x, y and z, solved by elimination down to one unknown, then back up.
Linear and Quadratic Simultaneous Equations Calculator
A line with a circle or a parabola: substitute, solve the quadratic, find both points.
Quadratic Inequalities Calculator
Solve ax² + bx + c < 0 and friends: find the roots, sketch the U, read off the region.
Iteration Calculator
Run xₙ₊₁ = f(xₙ) from a starting value until the answer settles to the decimal places you need.
Trial and Improvement Calculator
Solve x³ + px = q or 2ˣ = 20 by trying values, closing in, then testing the halfway value.
Composite and Inverse Functions Calculator
fg(x), gf(x) and f⁻¹(x) worked out from f and g, plus values like fg(2) from the inside out.
Equation of a Circle Calculator
Circle equations from a centre and radius, the centre and radius back out, and tangents.
Algebraic Fractions Calculator
Simplify by factorising, add or subtract over a common bottom, or solve an equation with fractions.
Data and Rates
Mean Median Mode Calculator
Mean, median, mode and range from any list, sorted first so the median is honest.
Speed Distance Time Calculator
The formula triangle for speed, density and pressure, fill two, find the third.
Probability Calculator
Single events, AND, OR and full trees, always as simplified fractions first.
Averages from a Table Calculator
Mean, median and mode from a frequency table, fx row built in front of you.
Interquartile Range Calculator
Quartiles and the IQR from any list, n plus one positions shown.
Time Calculator
Time between two times, add a duration, multiply one, or find 25% extra time.
Estimated Mean Calculator
The mean of grouped data, using the midpoint of every class interval.
Pie Chart Calculator
Turn any set of totals into pie chart angles that add up to 360 degrees.
Expected Frequency Calculator
How many times something should happen across a number of tries.
Capture Recapture Calculator
Estimate a whole population from a tagged sample caught twice.
Wage Calculator
Turn any pay rate into daily, weekly, monthly and yearly amounts.
Density Calculator
Density, mass and volume: fill in two and the third appears.
Pressure Calculator
Pressure, force and area, worked out from the same formula triangle.
Exam Planning
No calculator matches that search. Try a broader word, like "percentage" or "shape".
More SHLC Maths Tools
These live outside the calculator suite and are kept up to date separately.