Height Of Cylinder
Calculate the height of a cylinder from its volume and radius using h = V / (pir^2). Get instant results for any geometry or engineering problem.
About This Calculator
The Height Of Cylinder Calculator computes the height of a right circular cylinder from its volume and radius using the formula h = V / (pir^2), which rearranges the standard cylinder volume formula V = pir^2h to solve for height. This is one of the most common geometry calculations used across engineering, manufacturing, construction, and education worldwide.
This tool is useful for engineers determining the required height of a cylindrical tank with a given radius and capacity, students solving geometry problems, professionals in manufacturing and construction working with cylindrical containers, and anyone needing to calculate the dimensions of cylindrical objects. The calculation works with any consistent unit system -- whether you use meters and cubic meters, centimeters and cubic centimeters, or feet and cubic feet.
How the Formula Works
The volume of a right circular cylinder is given by V = pir^2h, where r is the radius of the circular base and h is the height. To find the height when volume and radius are known, we rearrange: h = V / (pir^2). This means height equals volume divided by the area of the base (pir^2). For example, a cylinder with volume 900 cubic units and radius 5 units has a height of 900 / (pi x 25) ≈ 11.46 units.
Related Geometry Calculations
The same inverse approach works for other cylinder parameters: if you need the radius from volume and height, use r = sqrt(V / (pih)), or for total surface area A = 2pir^2 + 2pirh. Our Radius Of Cylinder Calculator and Cylinder Volume Calculator handle these related conversions. All of these assume a right circular cylinder where the bases are parallel circles directly above each other.
Use consistent units throughout: if radius is in centimeters, volume must be in cubic centimeters and height will be in centimeters. The calculator does not perform unit conversion -- it works with whatever units you input, returning results in the corresponding linear unit.
Frequently Asked Questions
What is the formula for finding the height of a cylinder?
The formula to find the height of a cylinder from its volume and radius is h = V / (pir^2), where V is the volume, r is the radius, and pi ≈ 3.14159. This rearranges the standard volume formula V = pir^2h to solve for height.
What units should I use for volume and radius?
Use consistent units. If radius is in meters, volume should be in cubic meters (m^3) and height will be in meters. If radius is in centimeters, volume should be in cubic centimeters (cm^3) and height will be in centimeters.
Can I find the height from the diameter instead of the radius?
Yes, first convert diameter to radius by dividing by 2 (r = D/2), then use the same formula h = V / (pir^2). Or use our Cylinder Diameter calculator to convert first.
How do I find the height if I only know the surface area?
If you know the total surface area A and radius r, you can find the height using h = (A - 2pir^2) / (2pir). This comes from the surface area formula A = 2pir^2 + 2pirh rearranged for h.
What if I enter zero or negative values?
Volume and radius must be positive numbers. Zero or negative values are not physically meaningful for a cylinder and the calculator will not compute a result.
Is this height of cylinder calculator free?
Yes, all calculators on Calculy are completely free to use with no limits or registration required.
How accurate is the height calculation?
The calculation is mathematically exact using the formula h = V / (pir^2) with JavaScript double-precision floating point. Results are displayed rounded to two decimal places for readability, but the internal accuracy is to about 15 significant digits.
Does this work for oblique cylinders?
No, this calculator assumes a right circular cylinder where the bases are parallel circles directly above each other. For oblique cylinders (where one base is shifted), the vertical height differs from the slant height, and the formula h = V / (pir^2) does not apply.