Surface Area Calculator
Find the total and lateral surface area of six common 3D solids: with the formula, the slant height, and the substituted numbers shown.
Details
Surface area
54
in square units
This works out the surface area of a 3D shape: the total area of its outside, as if you unwrapped it and laid it flat.
Pick the shape and enter its measurements, and it returns the area in square units along with the formula it used.
What surface area is
Surface area is how much outside a shape has. Volume is how much fits inside. Wrapping paper is surface area; the space in the box is volume.
Because it measures a flat covering, the answer is always in square units — square metres, square feet — while volume is in cubic units.
This is the number you want for painting, wrapping, coating, plating, insulating, or working out how fast something loses heat. Volume is what you want for filling it.
Every face is a rectangle, and opposite faces match. So there are only three distinct areas to calculate, each counted twice.
What to enter
- Shape
- Cube, box, cylinder, cone, sphere, hemisphere or capsule. The measurements requested change to match.
- Radius
- For round shapes, the distance from the centre to the edge. Measure across and halve it.
- Height / length
- How tall or long the shape runs.
The formulas behind each shape
- Cube
- 6 × side². Six identical square faces.
- Box
- 2(lw + lh + wh). Three pairs of matching rectangles.
- Cylinder
- 2πr² + 2πrh. Two circular ends plus the wrapped side.
- Sphere
- 4πr². Exactly four times the area of the circle through its middle.
- Cone
- πr² + πrl, where l is the slant height, not the vertical height.
What this assumes
Shapes are perfectly regular and smooth. Real objects with texture have more actual surface than the maths says.
The full outside is counted. If a shape sits on the ground, you may not want the base included.
How to calculate surface area
Break the shape into faces you can measure, work out each, and add them up.
- flat faces
- Length × width for each rectangle
- curved surfaces
- Have their own formula, like 2πrh for a cylinder's side
Identify every face. A box has six. A cylinder has two circles and one curved wrap.
Work out each area. Use the same unit throughout, or the totals will not add correctly.
Add them together. The result is in square units.
Subtract anything not exposed. For painting a room, take out the doors and windows. For a tank on the ground, you may not need the base.
See a worked example: a sphere with a radius of 3
- Radius
- 3
Surface area of a sphere is 4πr².
r² = 9, so 4 × π × 9 = 36π.
That works out to 113.10 square units.
A curiosity: at radius 3, the volume is also 36π. That is a coincidence of this particular radius, not a rule — the two formulas grow at different rates.
113.10 square units
Frequently asked questions
Surface area is the outside, measured in square units. Volume is the inside, measured in cubic units.
Use surface area for paint, wrapping and coating. Use volume for how much a container holds.
Because area depends on two dimensions at once. Doubling every measurement makes the surface area four times larger, since 2 × 2 = 4.
Volume grows by eight, since 2 × 2 × 2 = 8. This is why large animals have proportionally less skin for their bulk than small ones, and why they lose heat more slowly.
The distance from the tip down the sloping side to the edge of the base, not the vertical height straight down the middle.
They are different, and the surface area formula needs the slant. If you only know the vertical height and the radius, find the slant with Pythagoras: l = √(r² + h²).
Divide the surface area by the coverage figure on the tin, usually given in square feet or metres per litre or gallon.
Then multiply by the number of coats and round up. The paint calculator handles walls, ceilings and the deductions for doors and windows.
It depends on the job. For wrapping a gift, yes. For painting a tank that sits on the ground, no.
This calculator gives the complete outside area, so subtract any face that is not actually exposed.
Problems people actually run into
Using the vertical height on a cone
The cone formula needs the slant height, measured along the sloping side. Substituting the vertical height gives an answer that is too small, and the gap grows as the cone gets wider.
Convert first: slant = √(radius² + height²). For a cone 3 across and 4 tall, the slant is 5, not 4.
Mixing square and cubic units
Surface area is square units and volume is cubic. Quoting a surface area in cubic feet, or ordering paint against a volume figure, is a surprisingly common slip.
The units are the check. If your answer came from multiplying three lengths together, it is a volume, whatever you meant to calculate.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026