Cone Surface Area Calculator
The surface area of a cone is A = π r (r + l), and this cone surface area calculator works it out the moment you enter a radius and a height or slant. You'll see the total surface area, the curved (lateral) surface area, and the base at once, in square inches, feet, centimeters, and meters, plus the answer in terms of pi. It handles a full cone or a frustum, open or closed, and it shows the formula and steps with every result.
- Total & curved area
- Cone or frustum
- Height or slant
- Without the base
- In terms of pi
Last updated June 15, 2026 Method: A = πr(r + l) Reviewed by the Calcowa math team
Enter a positive radius and height to see the surface area.
Show all units
A = π × 3 × (3 + 5) = 75.4 in²
What is the surface area of a cone?
The surface area of a cone is the area of its sloping side plus its round base, found with A = π × r × (r + l), where r is the base radius and l is the slant height. For a radius of 3 in and a slant of 5 in, the cone surface area is about 75.4 square inches.
That total has two parts: the curved side, πrl, and the circular base, πr². The slant height l is the distance up the slope, not the vertical height, so it's longer than the height. Two pieces, one skin.
How do you calculate the surface area of a cone?
To find the surface area of a cone, get the slant height, work out the curved side, then add the base. Here's the full sequence:
- 1
Measure the radiusMeasure the base radius. If you only have the diameter, divide it by 2.
- 2
Find the slant heightUse the slant directly, or find it from the height with l = √(r² + h²).
- 3
Curved areaMultiply pi by the radius by the slant for the curved (lateral) side.
- 4
Add the baseAdd the base circle, pi times radius squared, for the total surface area.
- 5
Convert the unitsConvert to square feet or square meters if that's what you need.
Curved (lateral) surface area of a cone
The curved surface area of a cone, also called the lateral surface area, is the sloping side on its own: CSA = π × r × l. Picture unrolling the side into a flat sector of a circle, and that sector's area works out to πrl. The calculator shows this curved value next to the total. For an open cone with no base, that's the whole answer. Same side, two names.
Surface area of a cone with the slant height
Surface area uses the slant height, not the vertical one, so that's the measurement you'll plug in. If you already have the slant l, set the height type to Slant and enter it: the curved area is πrl and the total is πr(r + l). If you only have the vertical height h, the calculator finds the slant with l = √(r² + h²) first, since the radius, height, and slant make a right triangle.
Surface area of a cone without the base
An open cone, like a funnel, an ice cream cone, or a party hat, has no bottom to cover, so you skip the πr² base and count only the curved side, πrl. It's the same as the lateral surface area. Use the curved value from the result panel when the base is open, and the full total when the base is closed.
Curved surface area of a frustum (truncated cone)
A frustum is a cone with the pointed top sliced off, like a lampshade or a bucket. Its curved surface area is a slanted band, CSA = π × (R + r) × l, where R is the bottom radius, r is the top radius, and l is the slant height of the band. Add the two circular ends, πR² and πr², for the total surface area.
Switch the calculator to Frustum and enter both radii with the height or slant. It'll work out the slant with l = √((R - r)² + h²) and add the band and the ends for you.
Surface area of a cone in terms of pi
For a math class you'll often want the answer in terms of pi, with π left as a symbol. Work out r(r + l) for the total and keep the pi: for r = 3 and l = 5 that's 3 × 8 = 24, so the surface area is 24π square units. The result panel shows this in-terms-of-pi value next to the decimal.
Surface area and volume of a cone
A cone's got two measures that often show up together. The surface area, A = πr(r + l), is the outer skin. The volume, V = (1/3)πr²h, is the space inside. They use different heights too: surface area needs the slant l, while volume needs the vertical h. For the space inside, switch to the cone volume calculator.
A surface area example, step by step
Say you've got a cone with a radius of 6 cm and a slant height of 10 cm. The curved side is π × 6 × 10 = about 188.50 square centimeters, and the base is π × 6² = about 113.10 square centimeters. Add them up.
A = π × 6 × (6 + 10) = 96π ≈ 301.59 cm²
curved 188.50 cm² + base 113.10 cm²
Enter a radius of 6 and a slant of 10 in centimeters above, and you'll get the matching square meters and square inches at once.
Units and accuracy
Calcowa shows the cone surface area in square millimeters, centimeters, meters, inches, feet, and yards at once, plus the exact answer in terms of pi. The results use the full value of pi, not a rounded 3.14, so they're accurate for engineering, school, and material estimates.
| Unit | Best for | Good to know |
|---|---|---|
| Square inches (in²) | Funnels, hats, small cones | Default when you enter inches |
| Square feet (ft²) | Roofs, hoppers, large cones | 1 ft² = 144 in² |
| Square centimeters (cm²) | Lab and school work | 1 in² = 6.4516 cm² |
| Square meters (m²) | Tanks, silos, big structures | 1 m² = 10.7639 ft² |
| In terms of pi (π) | Exact math answers | Leaves the result as a multiple of pi |
Frequently asked questions
Is the lateral surface area the same as the curved surface area of a cone?
Yes. Lateral surface area and curved surface area both mean the sloping side of the cone, πrl. Neither one includes the circular base, so for a closed cone you add πr² to get the total.
The total surface area of a cone is A = π × r × (r + l), where r is the base radius and l is the slant height. That splits into the curved side, πrl, plus the round base, πr². For r = 3 in and slant l = 5 in, the total is about 75.4 square inches.
The curved or lateral surface area is the sloping side on its own, πrl. The total surface area adds the circular base, πr², so TSA = πrl + πr². If the cone is open at the bottom, like a funnel, you only count the curved part.
If you already have the slant height l, you're set: the curved area is πrl and the total is πr(r + l). Set the calculator's height type to Slant, enter r and l, and it skips straight to the answer without needing the vertical height.
Leave off the πr² base circle and use only the curved part, A = πrl. That open-cone area is what you want for a paper funnel, a party hat, or a megaphone, where there's no bottom to cover.
A frustum is a cone with the top cut off, so its curved surface is a slanted band: CSA = π(R + r)l, where R and r are the two radii and l is the slant height. Add the two circular ends, πR² and πr², for the total. Switch to Frustum and enter both radii.
The slant height is l = √(r² + h²), since the radius, vertical height, and slant form a right triangle. If you have the vertical height, set the height type to Vertical and the calculator finds the slant for you.
From the slant height, the vertical height is h = √(l² - r²). From the volume, it's h = 3V ÷ (πr²). Either way, the radius, height, and slant always make a right triangle, so the Pythagorean theorem ties them together.
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