Cylinder Volume Using Radius

The radius is the distance from the center of the circular base to its edge. Pair it with the cylinder's height and this calculator applies V = πr²h to give you the volume instantly. This is the most direct way to find cylinder volume.

Volume Using Radius

V = πr²h
r V = π × r² × h

The Standard Radius Formula

r V = πr²h

V = π × r² × h is the foundation of every cylinder volume calculation. Here r is the radius of the circular base and h is the perpendicular height.

The formula works in two steps. First, r² gives the squared radius, and multiplying by π converts it into the area of the circular base (πr²). Second, multiplying that area by h stacks the circle through the full height, filling the 3D space.

Example: r = 7 cm, h = 15 cm. V = π × 49 × 15 = 2,309.07 cm³.

How to Find the Radius

measure Center to edge = r

If you can access the circular face of the cylinder, measure from the center to the edge. That's the radius directly.

If you only have the diameter (the full width across), divide by 2. If you have the circumference (the distance around), divide by 2π (approximately 6.2832).

For irregular cylinders or ones you can't easily measure, wrap a string around the base to get the circumference, then convert: r = C / (2π).

Radius vs Diameter: Which to Use

A B r vs d: use the right one

The formula expects the radius, not the diameter. If you plug in the diameter by mistake, your result will be 4× too large.

In practice, many measuring tools give you the diameter. Calipers measure across the full width. Rulers placed across a circle measure the diameter. Always divide by 2 before using the formula.

Some formulas are written with diameter: V = (π × d² × h) / 4. Both are equivalent — use whichever matches your measurement.

Frequently Asked Questions

What is the radius of a cylinder?
The radius is the distance from the center of the circular base to any point on its edge. It's half the diameter.
How do I find the radius if I know the volume and height?
Rearrange the formula: r = √(V / (π × h)). Divide the volume by (π × height), then take the square root.
Can the radius and height have different units?
No. Both must use the same unit (both in cm, both in inches, etc.). If they differ, convert one to match the other before calculating.
What if my cylinder base is not a perfect circle?
Measure the radius at several points around the base and use the average. If the base is an ellipse, use V = π × a × b × h, where a and b are the semi-axes.
Does the formula change for very tall or very short cylinders?
No. V = πr²h works regardless of proportions — whether the cylinder is tall and thin or short and wide.