Math Formulas
Every formula explained in plain English, with a diagram, a short proof, worked examples, and free practice.
Area, perimeter, and the shapes you meet every day.
- Area of a Circle - The area of a circle is pi times the radius squared. See what the formula means, why it works, worked examples, and free practice.
- Area of a Parallelogram - The area of a parallelogram is base times height. See what the formula means, why it works, worked examples, and free practice.
- Area of a Rectangle - The area of a rectangle is length times width. See what it means, why it works by counting squares, worked examples, and free practice.
- Area of a Trapezoid - The area of a trapezoid is one half the sum of the parallel sides times the height. See what it means, why it works, worked examples, and free practice.
- Area of a Triangle - The area of a triangle is half the base times the height. See what base and height mean, why the half is there, worked examples, and free practice.
- Circumference of a Circle - The circumference of a circle is pi times the diameter, or two times pi times the radius. See what it means, why pi appears, and free practice.
- Perimeter Formulas - Perimeter is the total distance around a shape. See the square, rectangle, and triangle formulas, why they work, worked examples, and free practice.
- The Pythagorean Theorem - The Pythagorean theorem says a squared plus b squared equals c squared for a right triangle. See what it means, why it works, worked examples, and free practice.
How much fits inside, and how much surface wraps around it.
- Volume of a Cylinder - The volume of a cylinder is pi times the radius squared times the height. See what it means, why it works, worked examples, and free practice.
Solving equations, lines, and the quadratic formula.
- The Quadratic Formula - The quadratic formula solves any equation of the form a x squared plus b x plus c equals 0. See what it means, why it works, worked examples, and free practice.
- The Slope Formula - The slope of a line is the rise over the run: the change in y divided by the change in x. See what it means, why it works, worked examples, and free practice.
Interest, percentages, and everyday money math.
- Compound Interest - Compound interest grows money by paying interest on interest. See the formula, what each part means, why it beats simple interest, and free practice.
- Simple Interest - Simple interest is principal times rate times time. See what each part means, why it works, worked money examples, and free practice.
The sine, cosine, and tangent ratios and how to use them.
- SOH-CAH-TOA (Sine, Cosine, Tangent) - SOH-CAH-TOA is the memory trick for the three trig ratios: sine, cosine, and tangent in a right triangle. See what each means, why it works, and free practice.
Averages, spread, and the chance of things happening.
- Mean, Median & Mode - Mean, median, and mode are the three ways to find the middle of a data set. See what each one means, how to find it, worked examples, and free practice.
Number patterns and the sums they build.
- Arithmetic Sequence Formula - The nth term of an arithmetic sequence is the first term plus (n minus 1) times the common difference. See what it means, why it works, and free practice.
Powers, roots, and logarithms made simple.
- Exponent Rules (Laws of Exponents) - The laws of exponents let you multiply, divide, and raise powers quickly. See each rule, why it works from plain counting, worked examples, and free practice.
Factors, primes, and divisibility.
- Divisibility Rules - Divisibility rules are quick tests that tell you if a number divides evenly by 2, 3, 4, 5, 6, 8, 9, or 10, with no long division. See every rule, why each works, and free practice.
Derivatives, integrals, and the rules that run them.
- The Power Rule (Derivatives) - The power rule is the fastest way to differentiate powers of x: bring the exponent down and subtract one. See what a derivative means, why the rule works, and free practice.