Area & Volume Calculator
Area and perimeter of flat shapes, volume and surface area of solids
Loading the tool…
Calculates the area and perimeter of flat shapes such as circles, triangles and trapezoids, and the volume and surface area of solids such as cylinders, spheres and cones, with a labelled drawing and the formulas.
How to use
- Choose "Flat shapes" or "Solids" and then click a shape. There are 12 flat shapes and 11 solids.
- Choose a "Unit": mm, cm, m, km, in, ft or yd.
- Enter the dimensions shown in the drawing, such as the radius r or the height h; the results appear at once.
- "Formulas" shows the equations used, and "Area in other units" or "Volume in other units" converts the result to units such as m², L or gallons.
How it works
- Area of a circle = πr², circumference = 2πr, volume of a cylinder = πr²h, volume of a cone = πr²h ÷ 3, volume of a sphere = 4πr³ ÷ 3, surface area of a sphere = 4πr².
- An ellipse perimeter has no simple formula and is calculated with the arithmetic-geometric mean (AGM) method; an ellipsoid surface uses numerical integration.
- 1 L = 1,000 cm³. Inches, feet and gallons are converted with their defined values.
Questions and answers
- How do I find the area of a circle?
- Square the radius and multiply by π. A circle with a radius of 5 cm has an area of π × 5² ≈ 78.54 cm².
- What is the formula for the volume of a cylinder?
- The base area times the height, πr²h. With a radius of 10 cm and a height of 20 cm the volume is about 6,283 cm³, or about 6.28 L.
- How do I find the area of a trapezoid?
- Add the two parallel sides, multiply by the height and divide by 2. With sides 4 and 6 and a height of 5, the area is 25.
- How do I find the area of a triangle from three sides?
- Choose "Triangle (three sides)"; it uses Heron's formula. A triangle with sides 3, 4 and 5 has an area of 6.