Radius Of Cylinder
Calculate the radius of a cylinder from its volume and height using r = sqrt(V / (pih)). Get instant results for any geometry or engineering problem.
About This Calculator
The Radius Of Cylinder Calculator computes the radius of a right circular cylinder from its volume and height using the formula r = sqrt(V / (pih)), derived from the standard cylinder volume formula V = pir^2h. Given any two of these three values (volume, height, and radius), the third can always be determined through algebraic rearrangement.
This tool is ideal for engineering students solving geometry problems, manufacturers determining the diameter of cylindrical tanks from their capacity, construction professionals calculating pipe dimensions from flow volume, and anyone working with cylindrical containers where the radius needs to be determined from known volume and height. The calculator supports any consistent unit system -- if height is entered in meters, the volume must be in cubic meters, and the resulting radius will be in meters.
The radius of a cylinder is the distance from the center of the circular base to its edge. For a right circular cylinder -- the most common type where the sides are perpendicular to the bases -- the relationship between volume V, radius r, and height h is given by V = pir^2h. Rearranging for r gives r = sqrt(V / (pih)). This formula works for any right circular cylinder regardless of its size, from microscopic capillaries to industrial storage tanks.
In practical applications, this calculation is used in numerous fields: packaging design to determine can dimensions from capacity requirements, plumbing to size pipes based on desired flow rates, manufacturing to create cylindrical parts from raw material volumes, and agriculture to determine silo dimensions from grain storage needs. The inverse square relationship between radius and height means that doubling the radius quadruples the volume, making this formula particularly useful for scaling cylindrical containers up or down while maintaining the same capacity.
For related calculations, try our Height Of Cylinder Calculator to find height from volume and radius, or the Cylinder Volume Calculator for volume from radius and height. If you need to work with surface area instead, check out the Surface Area Of Cylinder Calculator.
Frequently Asked Questions
What is the formula for finding the radius of a cylinder?
The formula to find the radius of a cylinder from its volume and height is r = sqrt(V / (pih)), where V is the volume, h is the height, and pi ≈ 3.14159. Rearranging the volume formula V = pir^2h gives this relationship.
What units should I use for volume and height?
Use consistent units for both inputs. If height is in meters, volume should be in cubic meters (m^3). If height is in centimeters, volume should be in cubic centimeters (cm^3). The result radius will be in the same linear unit (m or cm).
Can I find the radius from the diameter instead?
Yes, the radius is exactly half the diameter: r = D / 2. Use our Cylinder Diameter calculator to convert from radius to diameter or vice versa.
How do I find the radius if I know the surface area?
Finding the radius from surface area is more complex. For a right circular cylinder, total surface area A = 2pir^2 + 2pirh. This quadratic equation in r requires solving for r given A and h, which is beyond the scope of this calculator.
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 cylinder and the calculator will not compute a result.
Is this radius of cylinder calculator free?
Yes, all calculators on Calculy are completely free to use with no limits or registration required.
Can I calculate the radius using lateral surface area instead of volume?
Yes, if you know the lateral surface area and height, you can use r = A_l / (2pih). If you know the total surface area and height, use r = (sqrt(h^2 + 2A/pi) - h) / 2. Our calculator currently computes radius from volume and height, which is the most common use case.
How do I use this calculator with different unit systems?
Simply use consistent units for both inputs. For meters, enter height in meters and volume in cubic meters. For centimeters, enter height in cm and volume in cubic centimeters. The result radius will be in the same linear unit. Our calculator does not perform unit conversion, so ensure your inputs share the same unit system.