Guide

How to find the radius, diameter, or height of a cylinder from its volume

8 min read · geometry reference

If you already know how much a cylinder needs to hold — a tank's capacity, a mold's volume — and need to work out one of its dimensions, you're solving the volume formula in reverse. Here's every version of that, with the algebra shown so you can trust the result.

Start from the formula you already know

A cylinder's volume comes from multiplying the area of its circular base by its height:

V = π × r² × h

Normally you'd plug in r and h to find V. Reverse-solving means you know V and one of the dimensions, and you need to isolate the other. There are exactly three useful rearrangements, depending on what you already have.

Don't want to do the algebra by hand? The calculator handles all three reverse-solve modes instantly. Open the calculator

Finding the height when you know volume and radius

This is the most common reverse-solve — you know how much volume you need and the radius is fixed by your container or mold, and you need to know how tall to make it.

Starting from V = πr²h, divide both sides by πr²:

h = V / (π × r²)

Worked example

You need a cylindrical tank that holds exactly 5,000 cm³, and it has to fit a radius of 10 cm. How tall does it need to be?

h = 5,000 / (π × 10²) = 5,000 / (π × 100) = 5,000 / 314.16

h ≈ 15.92 cm

Finding the radius when you know volume and height

This direction comes up when the height is fixed — maybe by shelf space or a mold's depth — and you need to know how wide the cylinder must be to hit a target volume.

Starting from V = πr²h, divide by πh, then take the square root of both sides (since you're isolating r², not r):

r = √(V / (π × h))

The square root is the step people most often forget. Without it, you'd be solving for r², not r — and the number you'd get would be the wrong order of magnitude.

Worked example

A candle mold needs to hold 800 cm³ and the mold is 12 cm tall. What radius should the mold be?

r = √(800 / (π × 12)) = √(800 / 37.70) = √21.22

r ≈ 4.61 cm — so the mold's diameter should be about 9.21 cm.

Finding the diameter once you have the radius

This step is simpler — diameter is always exactly twice the radius, since the radius is measured from the center to the edge and the diameter spans the full width:

d = 2 × r

If you solved for radius using the formula above, just double it. If you need to go the other way — you have the diameter and need the radius — divide by 2 instead:

r = d / 2

This matters because the volume formula itself only uses radius, not diameter. If you're given a diameter and plug it directly into V = πr²h without halving it first, your answer will be 4 times too large — a mistake worth double-checking, since it's the single most common error in these calculations.

All three formulas, side by side

You know	Solving for	Formula
Volume (V), height (h)	Radius (r)	r = √(V / (π × h))
Volume (V), radius (r)	Height (h)	h = V / (π × r²)
Radius (r)	Diameter (d)	d = 2 × r
Diameter (d)	Radius (r)	r = d / 2

A quick sanity check for any reverse-solve

Once you have an answer, plug it back into the original formula — V = πr²h — using your solved value alongside the one you started with. If it doesn't return your original volume, recheck whether you squared (or square-rooted) the right variable. This single check catches almost every reverse-solve mistake before it costs you actual material or a wasted mold.

All four of these — solve for volume, height, radius, or surface area — are built into one calculator with live diagrams showing exactly which value is being solved for. Try the reverse-solve modes

If you're pouring concrete into a cylindrical form rather than working a pure geometry problem, the same reverse-solve logic applies to figuring out how much material you need — see the concrete cylinder calculator for cubic yards, bag counts, and weight.