Cone Surface Area Calculator — Lateral & Total
Enter the base radius and vertical height of a cone to find its slant height, lateral (curved) surface area, base area and total surface area.
units
units
Lateral surface + circular base: π·r·(l + r)
- 1
Slant height l
√(3² + 4²) = 5 - 2
Lateral surface area
π × 3 × 5 = 47.1239 - 3
Base area
π × 3² = 28.2743 - 4
Total surface area
47.1239 + 28.2743 = 75.3982
How does this calculator work?
A cone with base radius r and height h has slant height l = √(r² + h²). Lateral (curved) surface area = π·r·l; total surface area = π·r·(l + r). To exclude the base — e.g. for a funnel or open cone — use only the lateral area π·r·l.
Formula
How this is calculated
A right circular cone has a circular base of radius r, a vertical height h measured perpendicularly from the centre of the base to the apex, and a slant height l which is the straight-line distance from any point on the base circle to the apex. By Pythagoras, l = √(r² + h²).
The lateral (or curved) surface area is the area of the curved side, unrolled into a flat sector: π·r·l. The base is a circle with area π·r². Adding both gives the total surface area: π·r·l + π·r² = π·r·(l + r). If you need the surface area of an open cone (no base — e.g. a funnel or party hat), use only the lateral area π·r·l.
All formulas assume a perfect right circular cone with a flat circular base and a single apex directly above the centre. For oblique cones (apex off-centre) or frustums (truncated cones), different formulas apply. No approximations are used — π is taken to full double-precision.
Frequently asked questions
Lateral (curved) surface area = π·r·l covers only the sloping side. Total surface area adds the circular base (π·r²), giving π·r·(l + r). Use lateral area for open-top shapes like funnels or party hats; use total area for solid cones.
Apply Pythagoras in the right triangle formed by the radius (base), height (perpendicular leg) and slant height (hypotenuse): l = √(r² + h²). Enter r and h in the calculator and the slant height is shown automatically.
Yes — the formula π·r·l + π·r² applies only to a right circular cone where the apex is directly above the centre. For an oblique cone, the lateral surface area must be computed by integration and has no simple closed form.
TG we-Calculate Editorial Team. (2026). Cone Surface Area Calculator — Lateral & Total [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cone-surface-area-calculator
TG we-Calculate Editorial Team. "Cone Surface Area Calculator — Lateral & Total." TG we-Calculate. 2026. https://we-calculate.com/calculator/cone-surface-area-calculator.
TG we-Calculate Editorial Team, "Cone Surface Area Calculator — Lateral & Total," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cone-surface-area-calculator
@misc{wecalculate_cone_surface_area_calculator, title = {Cone Surface Area Calculator — Lateral & Total}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cone-surface-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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