About the Surface Area Calculator
Surface area is the total area of all the faces of a three-dimensional shape, and it tells you how much paint, wrapping or material you need to cover it. This surface area calculator works for seven common solids: a cube, a rectangular box, a sphere, a hemisphere, a cylinder, a cone and a square pyramid. You pick the shape, type its measurements and get the total surface area, the lateral (side) area where it applies, the base area, the slant height for cones and pyramids, and the volume. Use any one length unit for all measurements.
Updated October 2026
How to use the Surface Area Calculator
- 1Choose the shape from the list.
- 2Enter the measurements it asks for, such as radius and height.
- 3Use the same unit for every measurement.
- 4Optionally type the unit name so the answer is labelled.
- 5Read the total surface area, lateral area, base area and volume.
Formulas used
- Cube: 6a²; box: 2(lw + lh + wh)
- Sphere: 4πr²; hemisphere (solid): 3πr²
- Cylinder: 2πr(r + h)
- Cone: πr(r + s), where s is the slant height √(r² + h²)
- Square pyramid: a² + 2as, where s is √(h² + (a/2)²)
Practical uses
Surface area tells you how much paint covers a water tank, how much fabric wraps a gift box, how much metal sheet forms a can, and how fast a warm object loses heat. In packaging, a lower surface area for the same volume means less material, which is why many containers are close to cubes or cylinders. In science, a larger surface area makes reactions and cooling faster.
More geometry tools
Use the Volume Calculator for capacity, the Area Calculator for flat shapes, the Circle Calculator for radius and circumference and the Pythagorean Theorem Calculator for slant heights you want to check by hand. The Paint Calculator turns an area into litres or gallons of paint. For rounding long answers to a sensible number of digits, use the Rounding Calculator.
Features
- Seven common 3D shapes
- Total surface area
- Lateral (side) area and base area
- Slant height for cones and pyramids
- Volume shown with every shape
- Any unit, labelled for you
- Runs in your browser
Frequently asked questions
What is the surface area of a cube?
A cube has six equal square faces, so the surface area is 6 times the edge length squared. For an edge of 3 cm that is 6 times 9, which is 54 square centimetres. Its volume is the edge cubed, 27 cubic centimetres.
How do you find the surface area of a sphere?
The formula is 4 times pi times the radius squared. For a radius of 1 metre the surface area is about 12.57 square metres. The volume of the sphere is four thirds times pi times the radius cubed.
How do you find the surface area of a cylinder?
Add the two circular ends and the curved side. The total is 2 times pi times the radius times (the radius plus the height). A cylinder with radius 2 and height 5 has a surface area of about 87.96 square units. The curved side alone is 2 times pi times radius times height.
What is the difference between lateral and total surface area?
Lateral area counts only the side faces, leaving out the top and bottom. Total surface area includes the bases too. For painting the walls of a tank you would use the lateral area, and for painting the whole object you would use the total.
What is slant height?
The slant height is the distance along the sloping surface from the base to the tip of a cone, or from the middle of a base edge to the tip of a pyramid. It is longer than the vertical height and is found with the Pythagorean theorem. The tool calculates it for you.
Which units should I use?
Use the same unit for every measurement, such as all centimetres or all inches. The area is then in square units of that length and the volume in cubic units. If you mix units, such as radius in metres and height in centimetres, the result will be wrong.