EZ Calculators

Volume Calculator

This volume calculator works out the space inside ten solid shapes, from boxes and cylinders to cones, spheres and tubes. Pick the shape, enter its sizes in one unit, and get the volume in cubic units, liters and U.S. and Imperial gallons, with surface area too.

Calculation and content reviewed by EZ Calculators Editorial Team on .

Enter values

Change the fields below, then calculate to update the result.

Build the scenario below, then calculate for a complete result report.

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Choose an ideal solid

The dimension fields update with the shape. Curved solids use radius, not diameter.

Measured dimensions

For container capacity, measure the usable inside dimensions in one common unit.
Box length, cube side, prism length, or rectangular-pyramid base length.
m
Box width, rectangular-pyramid base width, or one perpendicular leg of a right-triangle cross-section.
m
Use the perpendicular dimension, not a cone or pyramid slant height.
m

Quantity and occupied share

Quantity multiplies identical solids. Occupied share applies to volume directly and must not be treated as liquid depth in a curved horizontal tank.
Multiply one ideal solid without re-entering its dimensions.
A percentage of calculated volume, not a liquid-depth measurement.
%

How do you calculate volume?

Multiply the area of the base by the height for boxes, prisms and cylinders. Cones and pyramids take one third of that. A cylinder with a 1 ft radius and 4 ft height holds pi x 1^2 x 4 = 12.57 cubic feet, about 94 U.S. gallons. A sphere uses 4/3 x pi x r^3 instead.

How to use the volume calculator

Pick the shape first. The fields change to match it, so a sphere asks only for a radius and a box asks for length, width and height. Use the same unit for every measurement.

Round shapes want the radius, which is half the diameter. Cones and pyramids want the straight-up height, not the length of the sloping side.

  1. Choose a shape: box, cube, cylinder, cone, sphere, hemisphere, triangular prism, rectangular pyramid, frustum or tube.
  2. Choose the unit: millimeters, centimeters, meters, inches, feet or yards.
  3. Enter the dimensions shown. For a container, use the inside measurements.
  4. Set how many identical solids you have, and an occupied percentage if you only want part of the total.
  5. Press Calculate volume to see the volume, surface area, the formula and a table of units.

Cone volume

A cone holds exactly one third of a cylinder with the same radius and height. A cone with a 3 inch radius and 10 inch height holds pi x 3^2 x 10 / 3 = 94.25 cubic inches. That's about 1.54 liters or 0.41 U.S. gallons.

If you measured the sloping side, that's the slant height, not h. The calculator shows the slant height in the result so you can compare it with your tape.

Formula guide
  • V = pi x r^2 x h / 3

Cylinder volume

Find the area of the circle, pi x r^2, then multiply by the height. A cylinder with a 1 foot radius and 4 foot height is pi x 1 x 4 = 12.57 cubic feet, or about 94 U.S. gallons.

Got the diameter instead? Halve it first. Entering a diameter as the radius makes the answer four times too big.

Formula guide
  • V = pi x r^2 x h

Sphere and hemisphere volume

A sphere's volume grows with the cube of its radius, so small radius errors grow fast. A ball with a 10 cm radius holds 4/3 x pi x 10^3 = 4,188.79 cubic centimeters, about 4.19 liters. Half of it, a hemisphere, holds 2,094.40 cubic centimeters.

Formula guide
  • Sphere: V = 4 x pi x r^3 / 3
  • Hemisphere: V = 2 x pi x r^3 / 3

Tank volume

For a full tank, match it to a shape. A rectangular tank is a box and an upright round tank is a cylinder. A tank measuring 48 x 24 x 24 inches inside holds 27,648 cubic inches, which is exactly 16 cubic feet or about 119.7 U.S. gallons.

The occupied percentage multiplies the full volume. It isn't a fill-depth gauge. In a horizontal cylinder, liquid a quarter of the way up fills only about a fifth of the tank, so don't type a depth reading into that box.

Pool volume

A rectangular pool with a flat floor is a box. A 32 x 16 foot pool, 5 feet deep, holds 2,560 cubic feet, which is about 19,150 U.S. gallons. A round above-ground pool is a cylinder: 24 feet across (12 foot radius) and 4 feet deep gives 1,809.56 cubic feet, about 13,536 gallons.

If the floor slopes evenly from end to end, enter the average depth. A pool running from 3 feet to 7 feet averages 5 feet, so the 32 x 16 example still holds 2,560 cubic feet. Measure to the water line, not the deck, for the water you'll add.

Worked volume examples from the calculator
Shape and sizeVolumeLitersU.S. gallons
Cone, r 3 in, h 10 in94.25 in^31.540.41
Cylinder, r 1 ft, h 4 ft12.57 ft^3355.8494.00
Sphere, r 10 cm4,188.79 cm^34.191.11
Tank, 48 x 24 x 24 in16 ft^3453.07119.69
Pool, 32 x 16 x 5 ft2,560 ft^372,491.1319,150.13
Round pool, r 12 ft, h 4 ft1,809.56 ft^351,240.9613,536.43

Formulas for every shape

Here r is radius, R the larger radius, h the perpendicular height, and l, w and a are straight lengths. For the triangular prism, b and t are the two legs that meet at the right angle, and L is the prism's length.

Formula guide
  • Box: V = l x w x h; cube: V = a^3
  • Right triangular prism: V = L x b x t / 2
  • Rectangular pyramid: V = l x w x h / 3
  • Conical frustum: V = pi x h x (R^2 + R x r + r^2) / 3
  • Tube material: V = pi x (R^2 - r^2) x h

Limits and when to double-check

These are ideal shapes. Real tanks have rounded corners, domed ends and fittings. Pools have steps and coves. Treat the answer as an estimate and use the maker's rated capacity when you have it. Tube mode gives the volume of the tube wall, not the space inside it.

Measurement errors grow. A 1% error in the radius means about 2% error in a cylinder and about 3% in a sphere. Measure at a few spots, and for pressure vessels, chemicals or structural work, rely on approved drawings and a qualified reviewer.

Sources

These references back the formulas and unit definitions on this page.

OpenStax: geometric formulasPublished volume and surface area formulas for common solids.OpenStax: determining volumes by slicingDerives the cylinder, cone, pyramid and sphere volume formulas.NIST: SI units for volumeDefines the cubic meter, liter and milliliter relationships.NIST SP 811 Appendix B.8 conversion factorsExact factors for U.S. gallons, Imperial gallons and cubic units.

FAQ

How many gallons are in a cubic foot?

About 7.48 U.S. liquid gallons. That's why the 2,560 cubic foot pool example works out to about 19,150 gallons. An Imperial gallon is larger, so a cubic foot holds about 6.23 of those.

How do I find the volume of a cylinder from the diameter?

Halve the diameter to get the radius, then use pi x r^2 x h. A 2 foot wide, 4 foot tall cylinder has a 1 foot radius and holds about 12.57 cubic feet.

Why is a cone one third of a cylinder?

A cone tapers evenly to a point, and stacking its thin circular slices adds up to exactly one third of a cylinder with the same base and height. Pyramids follow the same rule against boxes.

How do I calculate the volume of a rectangular tank?

Multiply inside length by width by height in one unit. A 48 x 24 x 24 inch tank holds 27,648 cubic inches, which is 16 cubic feet or about 119.7 U.S. gallons.

How much water is in my pool?

Multiply length by width by average depth for a rectangular pool, or pi x r^2 x depth for a round one. Then multiply cubic feet by about 7.48 to get U.S. gallons.

Can this tool work out a partly filled horizontal tank?

Not from a depth reading. The occupied percentage applies to total volume, and a horizontal cylinder's volume doesn't change in step with the liquid height. You need a dedicated partial-fill formula for that.

What is the volume of a sphere with radius 10 cm?

It's 4/3 x pi x 10^3, which is about 4,188.79 cubic centimeters or 4.19 liters. Double the radius to 20 cm and the volume grows eight times, to about 33.5 liters.