Results update as you type, with the formula and your own numbers in the working.
Slope and the equation of a line
The slope is the rise over the run: m = (y₂ − y₁) ÷ (x₂ − x₁). Through (1, 2) and (3, 5) it is 3 ÷ 2. The intercept b comes from y₁ − m × x₁, giving y = (3/2)x + 1/2. The slope and intercept stay as exact fractions when your points are whole numbers, decimals or fractions. When both x values match the line is vertical, its slope is undefined and its equation is x = a number; when both y values match the slope is 0.
The Pythagorean theorem
In a right triangle the two shorter sides a and b and the longest side c, the hypotenuse opposite the right angle, always satisfy a² + b² = c². So c = √(a² + b²), and a missing short side is √(c² − b²). The hypotenuse must be longer than either other side, otherwise there is no such triangle. Roots that do not come out whole are shown in simplest form, like 3√2, as well as a decimal.
Area, perimeter, volume and surface area
Area is measured in square units and volume in cubic units, so the unit you pick for the lengths carries through: centimetres give cm² and cm³. For volumes, 1,000 cm³ is 1 litre and one US gallon is 3.785 litres. A triangle’s area from three sides uses Heron’s formula. An ellipse has no exact simple perimeter formula, so Ramanujan’s close approximation is used. A hemisphere’s surface area includes its flat base.
Privacy
The sums run in your browser. Nothing you type is sent anywhere.