HesapHanem

Cone Surface Area Calculator

Find the surface area of a cone.

Result

282.74 units²
204.20 units²
13.00

How it is calculated

A cone has a circular base and a curved side. The slant height is found from the right triangle formed by radius and height: s = √(r² + h²). The curved (lateral) area is L = π·r·s, and the total surface area adds the base: A = π·r² + π·r·s = π·r·(r + s). Radius r is the base radius and h is the straight height from base to tip, not the slant. Both must be above zero and use the same length unit; areas come out in that unit squared (shown as units²), rounded to two decimals.

Worked example

Take r = 5 and h = 12. Slant height: √(25 + 144) = √169 = 13. Lateral area: π × 5 × 13 = 204.20. Base area: π × 25 = 78.54. Total: 204.20 + 78.54 = 282.74 units². If the units are centimetres, the cone needs about 282.74 cm² of material to cover its whole surface, base included.

Try this example →

Common mistakes

  • Entering the slant height in the height field. The height must be perpendicular to the base; the slant is calculated for you.
  • Using the diameter instead of the radius, which makes the area four times too large.
  • Forgetting the base when the question asks for total surface area. Lateral area is only the curved part.
  • Mixing units, such as radius in centimetres and height in metres.
  • Using this for an open cone or a cut-off cone (frustum); the formula covers a complete, closed cone only.

About this calculator

This calculator finds a cone's slant height using the Pythagorean relation l = √(r² + h²), then computes lateral surface area as π·r·l and total surface area as π·r·(r + l) — the lateral term unrolls the cone's curved side into a flat circular sector, while adding π·r² accounts for the circular base.

Geometry students solving surface-area problems, engineers and sheet-metal fabricators calculating material needed for conical parts like funnels, chutes, or roof caps, and hobbyists figuring out paper or fabric needed for a cone-shaped craft (party hats, lampshades) use this.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    If you are cutting a cone from flat sheet, the curved part unrolls into a circular sector whose radius is the slant height. Its opening angle is 360 times the base radius divided by the slant height. With r = 5 and h = 12 the slant is 13, so the sector is about 138.5 degrees. Add seam allowance on top, since the result is the exact surface only. What are you making with it: a funnel, a hat, a roof cap?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators