How to use the surface area calculator
- Choose the shape.
- Choose the length unit you measured in.
- Enter the measurements. For a cone or pyramid, the height is the straight-up height from the base to the tip, not the length of the sloping side; the calculator works out the slant for you.
- Read the total surface area, the lateral (side) area and the area of the flat faces, with the working underneath.
Surface area formulas
Lateral area is the area of the sides only, leaving out the top and bottom (or the base). Total surface area adds the flat faces back in. For a cone and a pyramid, s is the slant height: the distance along the sloping face, found with the Pythagorean theorem from the height and half the base. For a tube, D and d are the outer and inner diameters and L the length; the total counts the outside, the inside and the two ring-shaped ends.
Worked example
The calculator starts with a box 4 ft long, 3 ft wide and 2 ft high:
- The three different faces are 4 × 3 = 12 ft², 4 × 2 = 8 ft² and 3 × 2 = 6 ft²
- Each one appears twice, so the total is 2 × (12 + 8 + 6) = 52 ft²
- The lateral area (the four sides) is 2 × 2 × (4 + 3) = 28 ft², and the top and bottom add 2 × 12 = 24 ft²
- In square meters: 52 × 0.09290304 = 4.83096 m²
A cone with a 3 m radius and 4 m height has a slant height of √(9 + 16) = 5 m, so its total area is π × 3 × 5 + π × 3² = 15π + 9π = 24π = 75.3982 m².
Which area do you need?
| Job | Area to use |
|---|---|
| Wrapping a gift box | Total |
| Painting the walls of a room | Lateral of the box (minus doors and windows) |
| Label on a can | Lateral of the cylinder |
| Paint for a closed tank | Total |
| Fabric for a cone-shaped lampshade | Lateral of the cone |
| Insulating a pipe | Outer surface of the tube |
Buy extra material for overlap and waste. Wrapping paper needs a few inches of overlap on each seam, and paint coverage figures on the can assume a smooth surface. Two coats double the area you are covering.
Surface area and volume
Surface area grows with the square of the size, but volume grows with the cube. Double every side of a box and its surface area becomes 4 times larger while its volume becomes 8 times larger. That is why small objects cool down faster than large ones: they have more surface for each unit of volume. You can compare the two for any shape with the volume calculator.
Frequently asked questions
What is the difference between lateral and total surface area?
Lateral area covers only the sides of a solid. Total surface area also includes its flat ends or base. A cylinder 10 cm tall with a 3 cm radius has a lateral area of 60π = 188.496 cm² and a total of 78π = 245.044 cm² once the two circles are added.
Does a sphere have a lateral area?
A sphere has no flat faces or edges, so the idea of "sides" doesn't apply and its whole surface counts as curved. Its total surface area is 4πr², exactly four times the area of a circle with the same radius.
What is the slant height of a cone?
It is the distance from the tip of the cone down its side to the edge of the base. With radius r and height h, the slant height is √(r² + h²). A cone 4 m tall with a 3 m radius has a slant height of 5 m.
What units is surface area measured in?
Surface area is always in square units, the length unit you measured in multiplied by itself. If you measured in feet, the answer is in square feet. Use the table under the result to convert it.
Related calculators
- Volume Calculator — Volume of a cube, box, cylinder, cone, sphere, pyramid, capsule or tube, in cubic units, liters and gallons.
- Area Calculator — Area of a square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram, sector or regular polygon.
- Circle Calculator — Radius, diameter, circumference and area from any one of them, plus arc length and sector area for an angle.
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