Radius of a Cone Calculator
Given the height of a right circular cone and one other measurement — volume, lateral surface area, or total surface area — this calculator finds the base radius, slant height, and all remaining cone properties.
Solve radius from
units
cu units
Radius of the circular base of the cone
r = 7.071
- 1
Multiply volume by 3
3 × 523.6 = 1,570.8 - 2
Divide by π × h
1,570.8 ÷ (π × 10) = 50.000117 - 3
Radius = √(3V / (πh))
√50.000117 = 7.0711
How does this calculator work?
For a right circular cone with known height h: radius from volume = √(3V/(πh)), radius from total surface area = A/√(π²h²+2πA). The slant height l = √(r²+h²). All other cone properties (volume, lateral area, total area) are then computed from the derived radius and height.
Formula
How this is calculated
A right circular cone has three independent measurements: base radius r, height h, and slant height l = √(r² + h²). The volume is V = (1/3)πr²h and the lateral surface area is A_lat = πrl; the total surface area adds the base disk: A_total = πrl + πr².
When the volume and height are known, r = √(3V/(πh)) is a direct formula. When the lateral surface area and height are known, substituting l = √(r² + h²) leads to a quartic in r that reduces to a quadratic in r² — the positive root gives the radius. For the total surface area, a cleaner closed-form exists: r = A_total / √(π²h² + 2πA_total), derived by isolating r from the full expansion.
All formulas assume a perfect right circular cone (apex directly above the centre of the base). Enter consistent units — the radius and height will share the same unit, volume will be in that unit cubed, and surface areas in that unit squared.
Frequently asked questions
The slant height l is the distance from the apex to any point on the edge of the base circle, measured along the surface. By the Pythagorean theorem, l = √(r² + h²). It is not the same as the vertical height h.
The lateral surface, when unrolled, forms a flat sector of a circle whose radius is the slant height l. The arc length of that sector equals the base circumference 2πr, giving area = πrl. Using vertical height h instead would give the wrong result.
Rearrange V = (1/3)πr²h to h = 3V/(πr²). This calculator solves for radius given height; for other combinations, use a cone calculator that lets you pick the two known quantities.
Also known as
TG we-Calculate Editorial Team. (2026). Radius of a Cone Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/radius-of-cone-calculator
TG we-Calculate Editorial Team. "Radius of a Cone Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/radius-of-cone-calculator.
TG we-Calculate Editorial Team, "Radius of a Cone Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/radius-of-cone-calculator
@misc{wecalculate_radius_of_cone_calculator, title = {Radius of a Cone Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/radius-of-cone-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?