Results update as you type, with the formula and your own numbers in the working. Find the slope of a line, the missing side of a right triangle, and the area or volume of common shapes. It is free and private.
How to use the calculator
- Choose a tab: Slope of a line, Pythagoras, Area or Volume.
- Pick the Length unit: mm, cm, in or ft.
- Slope: enter Point 1 and Point 2.
- Pythagoras: enter two of the sides of the Right triangle and leave the third empty.
- Area or Volume: choose the Shape, then enter the Measurements.
- Read the answer and the working.
Shapes for area include the rectangle, square, triangle (from base and height, or from three sides), circle, trapezoid, parallelogram, ellipse and circle sector. Solids include the cube, rectangular box, cylinder, sphere, hemisphere, cone and square pyramid.
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.
Tips for accurate answers
- Measure everything in the same unit before you enter it.
- Check that the shape matches the formula. A room that is not a rectangle may need to be split into parts.
- Add a little extra to the area when buying paint, flooring or fabric, to allow for waste.
- Use the working to check your own homework steps.
Who uses it
Students, DIYers measuring a room or a garden bed, makers planning materials, and anyone sizing a container. For more maths help, try the equation solver and the graphing calculator.
Privacy
The sums run in your browser. Nothing you type is sent anywhere.
Questions
Why is the slope undefined?
A vertical line has the same x value at both points, so the run is zero and the slope cannot be worked out.
How do I convert cubic centimetres to litres?
1,000 cm³ is 1 litre.
Why is the hypotenuse error shown?
The longest side must be longer than both other sides. Check which side is c.