Lateral Area of a Cone Calculator — A = πrl
Enter the base radius plus either the perpendicular height or slant height of a right circular cone to get its lateral (curved) surface area, base area, total surface area and volume.
Known dimensions
units
units
A_lateral = π × r × l (curved surface only, no base)
47.12 u²
- 1
r² + h²
3² + 4² = 25 - 2
Slant height
l = √(r² + h²) = √25 = 5 - 3
Lateral area
π × r × l = π × 3 × 5 = 47.1239Unrolled cone = a flat sector of radius l and arc 2πr.
How does this calculator work?
The lateral surface area of a right circular cone (curved part only) is A = π·r·l, where r is the base radius and l = √(r² + h²) is the slant height. For a cone with r = 3, h = 4: l = 5, A = π × 3 × 5 ≈ 47.12 square units. Add π·r² for the total surface area.
Formula
How this is calculated
The lateral surface area of a right circular cone is the area of the curved outer surface, excluding the flat circular base. The key insight is to imagine cutting the cone from apex to base along one straight line and unrolling it flat: you get a sector of a circle whose arc length equals the base circumference (2πr) and whose radius equals the slant height l. The area of that sector is π·r·l.
The slant height l is the straight-line distance from the apex to any point on the base rim. If you know the perpendicular height h and the base radius r, Pythagoras gives l = √(r² + h²). Alternatively you can input l directly. Adding the base circle (π·r²) to the lateral area gives the total surface area π·r·(l + r), which is the amount of material needed to cover the entire outside of the cone.
All formulas apply to a right circular cone — one where the apex lies directly above the centre of the base. Oblique cones require different treatment. Results are in square units matching your input unit (e.g., cm² if you enter cm).
Frequently asked questions
Lateral surface area (π·r·l) covers only the curved slant surface of the cone, not the base. Total surface area (π·r·l + π·r²) adds the flat circular base. Use lateral area when the base is open (e.g., an ice-cream cone or funnel); use total area when the base is solid and you need to cover the whole outside.
By Pythagoras: the slant height l = √(r² + h²). For example, a cone with radius 3 and height 4 has slant height √(9 + 16) = √25 = 5 units.
A cone's surface is a ruled surface: all the straight lines from the apex to the base rim have equal length (the slant height l). When you unroll it, each such line becomes a radius of a flat sector, and the base circumference (2πr) becomes the arc. The sector has radius l and arc length 2πr, which gives it an area of (1/2)·l·2πr = π·r·l.
Also known as
TG we-Calculate Editorial Team. (2026). Lateral Area of a Cone Calculator — A = πrl [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lateral-area-of-cone-calculator
TG we-Calculate Editorial Team. "Lateral Area of a Cone Calculator — A = πrl." TG we-Calculate. 2026. https://we-calculate.com/calculator/lateral-area-of-cone-calculator.
TG we-Calculate Editorial Team, "Lateral Area of a Cone Calculator — A = πrl," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lateral-area-of-cone-calculator
@misc{wecalculate_lateral_area_of_cone_calculator, title = {Lateral Area of a Cone Calculator — A = πrl}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lateral-area-of-cone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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