Radius Of Cone
Calculate the radius of a right circular cone from its volume and height using r = sqrt(3V / (pih)). Free online 3D geometry calculator for students and professionals.
About This Calculator
The Radius Of Cone Calculator computes the radius of a right circular cone from its volume and height using the formula r = sqrt(3V / (pih)), derived from the standard cone volume formula V = (1/3)pir^2h. Given any two of these three values, the third can always be determined.
This tool is ideal for geometry students solving 3D shape problems, engineers determining the dimensions of conical tanks and hoppers, construction professionals working with tapered concrete forms, and anyone who needs to find the base radius of a cone from known volume and height measurements.
The calculator also displays the diameter (D = 2r), since diameter is often more practical for real-world applications like pipe fitting and manufacturing. For related calculations, try our Cone Volume Calculator to find volume from radius and height, or the Height Of Cone Calculator for height from volume and radius.
Frequently Asked Questions
What is the formula for finding the radius of a cone?
The formula to find the radius of a cone from its volume and height is r = sqrt(3V / (pih)), where V is the volume, h is the height, and pi ≈ 3.14159. This is derived by rearranging the cone volume formula V = (1/3)pir^2h to solve for r.
What units should I use for volume and height?
Use consistent units for both inputs. If height is in metres, volume should be in cubic metres (m^3). If height is in centimetres, volume should be in cubic centimetres (cm^3). The resulting radius will be in the same linear unit (m or cm).
Can I find the radius from the slant height instead?
Yes, if you know the slant height (l) and vertical height (h), you can find the radius using the Pythagorean theorem: r = sqrt(l^2 - h^2). This calculator uses the volume method, but our Slant Height Of Cone calculator can help with related cone dimension problems.
How do I find the diameter of a cone from its radius?
The diameter of a cone is exactly twice its radius: D = 2r. This calculator automatically displays the diameter alongside the radius for your convenience.
What happens if I enter zero or negative values?
Volume and height must be positive numbers to calculate a meaningful radius. Zero or negative values are not physically valid for a real cone and the calculator will not compute a result.
Is this radius of cone calculator free?
Yes, all calculators on Calculy are completely free to use with no limits or registration required.