Pick a shape, enter its dimensions in any mix of units, and get the total surface area with each part broken out.
Surface area is the total area of the outside of a solid shape, measured in square units. It answers practical questions: how much paint covers a tank, how much wrapping paper a box needs, how much sheet metal makes a can, or how much material a tent uses. Choose a shape above, enter its dimensions, and the calculator shows the total and, where it helps, the separate parts such as top, bottom and sides, so you can leave out the part you do not need.
A closed cylinder with a radius of 3 m and a height of 5 m has a top and bottom of π × 3² = 28.27 m² each, and a curved side of 2 × π × 3 × 5 = 94.25 m². The total is 28.27 + 28.27 + 94.25 = 150.80 m². If the tank is open at the top, or you are not painting the bottom, simply drop that part from the total. For a cube with an edge of 3 m, the answer is 6 faces × 3² = 54 m², and a rectangular box with sides 2, 3 and 4 m has 2 × (2×3 + 2×4 + 3×4) = 52 m².
The sloping side of a cone or pyramid is longer than its vertical height. The calculator finds that slant height for you from the right triangle made by the height and the base radius (for a cone), or the height and half the base edge (for a square pyramid). For a cone with a radius of 3 m and height of 4 m, the slant height is √(3² + 4²) = 5 m, so the sloping side has an area of π × 3 × 5 = 47.12 m² and the total with the base is 75.40 m². If you want to see that triangle yourself, the Right Triangle Calculator will solve it.
A spherical cap is a dome cut from a ball. Its curved part has an area of 2 × π × h × R, and the flat base adds π × r², and as in the volume calculator you can enter any two of the three dimensions. An ellipsoid is a stretched ball, and unlike every other shape here its surface area has no simple exact formula. The calculator uses a well-known approximation that stays within about 1% of the true value, and marks the result as approximate.
Surface area tells you how much material covers the outside, and volume tells you how much fits inside. The two scale differently: doubling every length multiplies the area by 4 but the volume by 8, which is why large containers store more per unit of material than small ones. To work out costs, multiply the area by the price per square metre of the material, and add a few percent for waste. For flat surfaces like floors and walls, the Area Calculator and Tile Calculator are more direct, and for sloping roofs the Roofing Calculator accounts for the pitch.
Using the diameter instead of the radius is the most common one, and it makes a round shape’s area four times too large. Another is forgetting which faces are actually included: a closed can has a top and bottom, but a bucket does not. And when a dimension is given as a slant length, check whether the formula wants the vertical height or the slant, because mixing them up changes the answer. The Pythagorean Theorem Calculator converts between the two when you know the base.
Add the two circular ends and the curved side: A = 2πr² + 2πrh.
Lateral surface area is only the sides, without the top and bottom. Total surface area includes every face.
A = 4 × π × r². Doubling the radius makes the area four times larger.
There is no simple exact formula for the surface area of an ellipsoid with three different axes, so the calculator uses a standard approximation that is accurate to about 1%.
Work out the area to be painted, then divide by the coverage printed on the paint can (often around 10 square metres per litre per coat) and multiply by the number of coats.
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