Geometry

Cylinder Volume Calculator

What this does

Compute cylinder volume from radius and height, with total surface area and base area alongside.

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Calculator inputs

How to use it

Using the cylinder volume calculator

  1. 01

    Measure radius and height

    Radius across the circular end through center; height along the axis.

  2. 02

    Read the volume

    In cubic units; divide by 231 for gallons from inches, or 1000 for liters from centimeters.

  3. 03

    Check surface area

    Useful for estimating sheet metal, labels or paint.

Good to know

Tanks, cans and pipes

Cylinders dominate storage because they are cheap to make, strong under pressure and easy to roll from flat stock. Water heaters, propane tanks, shipping drums and every can in your pantry share this geometry.

Capacity conversions worth knowing

  • Cubic inches ÷ 231 = US gallons.
  • Cubic centimeters ÷ 1000 = liters.
  • Cubic feet × 7.48 = US gallons.

How it's calculated

The math behind this calculator

V = πr²h A = 2πr(h + r)

A cylinder is a stack of identical circular disks: base area πr² times height h gives volume directly. Total surface area wraps two circles plus an unrolled rectangle of width equal to the circumference (2πrh); combined here as 2πr(h + r).

Both dimensions matter differently: volume scales linearly with height but quadratically with radius, so widening beats heightening for pure capacity gains.

Assumptions & limitations

  • Right circular cylinder; flat, parallel ends.
  • Interior dimensions if computing usable capacity.
  • Consistent units throughout; volume in cubic units.

Worked example

A tank of radius 2 and height 5 holds about 62.83 cubic units and needs about 87.96 square units of material to enclose.

FAQ

Frequently asked questions

Should I use inside or outside dimensions?
Inside for actual capacity, outside for shipping footprints. Wall thickness subtracts surprisingly much in small cylinders.
Does orientation affect volume?
Never; a cylinder holds the same lying down as standing; only the fill-level math changes.
How full is a partially filled horizontal tank?
Not a simple fraction; circular segment geometry applies. This tool covers the full-volume case.
What if I know circumference instead of radius?
Divide circumference by 2π to recover the radius, then proceed normally.

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