Volume Calculator and Estimator
Find the volume of a box, cylinder, sphere, cone or eight other shapes, see the formula worked through, and read the answer in cubic feet, gallons, liters or any other unit. Switch to the tank tab for liquid in a partly full tank, or to boxes for the CBM and dimensional weight of a shipment.
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How to use it
- Choose a shape, a tank, or a list of boxes.
- Pick the unit you measured in and type the sizes. Tick the diameter box if you measured across the circle.
- Choose the unit for the answer, such as gallons or cubic feet. Every other unit is listed below it.
- Pick a material to see what the volume weighs, then copy the result.
Why use this tool
12 shapes with the formula
Box, cube, cylinder, sphere, dome, cone, bucket, pyramid, prism, capsule, egg shape and pipe wall, each with the formula and surface area.
Partly full tanks
Upright and horizontal cylinders, rectangular and round tanks. Enter the dipstick depth to get gallons left and the fill level.
CBM and dimensional weight
List carton sizes and counts to get total cubic meters, cubic feet, chargeable weight for couriers and container fill.
Every unit at once
Cubic feet, cubic yards, US and imperial gallons, liters, quarts, cups, fluid ounces, barrels and acre-feet.
Weight of the contents
Water, fuel, concrete, sand, gravel, topsoil, mulch, steel and more, or your own density.
Diameter or radius
Measure across a pipe or tank and tick one box; the calculator halves it for you.
Volume formulas for common shapes
Volume is the space inside a solid. For anything with straight sides you multiply the area of the base by the height; for round shapes π (about 3.14159) appears because the base is a circle.
Use the same unit for every measurement. If you mix feet and inches, convert first, or let the calculator do it by picking one unit and typing decimals such as 2.5 ft.
| Shape | Formula | Example |
|---|---|---|
| Box | V = l × w × h | 4 × 3 × 2 ft = 24 ft³ |
| Cube | V = a³ | 3³ = 27 in³ |
| Cylinder | V = π r² h | r 1 ft, h 4 ft = 12.57 ft³ |
| Sphere | V = 4/3 π r³ | r 5 in = 523.6 in³ |
| Cone | V = 1/3 π r² h | r 3 in, h 9 in = 84.8 in³ |
| Pyramid | V = 1/3 l w h | 6 × 6 × 4 ft = 48 ft³ |
| Triangular prism | V = 1/2 b h l | b 4, h 3, l 10 ft = 60 ft³ |
How to convert cubic feet to gallons and liters
One cubic foot holds 7.48 US gallons or 28.32 liters. One cubic yard is 27 cubic feet, the unit used for concrete, mulch and topsoil deliveries. A US gallon is 231 cubic inches; an imperial gallon is about 20% larger at 4.546 liters.
To get gallons from inches, multiply length × width × height in inches and divide by 231. A 30 × 12 × 12 inch aquarium holds 4,320 in³, or about 18.7 gallons before you subtract gravel and decorations.
| From | To | Multiply by |
|---|---|---|
| Cubic feet | US gallons | 7.4805 |
| Cubic feet | Liters | 28.317 |
| Cubic yards | Cubic feet | 27 |
| Cubic inches | US gallons | ÷ 231 |
| Liters | US gallons | 0.26417 |
| Cubic meters | Cubic feet | 35.315 |
Liquid in a horizontal tank
Fuel oil, propane and water tanks lying on their side don't fill evenly: the first and last inches of a round tank hold far less than the middle. That is why a tank that reads half on the dipstick is half full, but a quarter of the height is only about 20% of the capacity.
The calculator uses the circular segment formula for horizontal cylinders and the spherical cap formula for round tanks, so the gallons left are exact for the inside dimensions you enter. Dished or rounded tank ends add a little extra volume that a plain cylinder does not include.
CBM and dimensional weight for shipping
Freight forwarders quote ocean and air shipments by CBM, short for cubic meters. Measure each carton in centimeters, multiply length × width × height and divide by 1,000,000 to get its CBM, then multiply by the number of cartons.
Couriers such as UPS, FedEx and DHL charge for whichever is larger, the scale weight or the dimensional weight. Dimensional weight is the volume in cm³ divided by 5000, or in inches, cubic inches divided by 139 for pounds. A 24 × 16 × 12 inch box therefore bills as 34 lb even if it weighs 10.
- 20 ft container: about 33 m³ inside, around 28 m³ of cartons in practice.
- 40 ft container: about 67 m³ inside, around 58 m³ of cartons.
- 40 ft high cube: about 76 m³ inside, around 65 m³ of cartons.
Estimating materials by volume
Landscape and building materials are sold by the cubic yard or by the ton. Measure the bed or hole as a box, enter the depth in inches with the unit set to inches, and choose the material to see the weight. Topsoil weighs about 1.1 tons per cubic yard, gravel about 1.4 tons and concrete about 2 tons.
Order 5 to 10% more than the exact volume: material settles, edges are rarely square and a short delivery costs more than the extra.
Frequently asked questions
How do I calculate volume in cubic feet?
Measure length, width and height in feet and multiply them. If you measured in inches, multiply the three numbers and divide by 1,728, because one cubic foot is 12 × 12 × 12 inches.
How many gallons are in a cubic foot?
One cubic foot is 7.48 US gallons or 6.23 imperial gallons. Multiply cubic feet by 7.48 to get US gallons.
How do I find the volume of a cylinder?
Multiply π by the radius squared and by the height: V = π r² h. If you measured the diameter, halve it first, or tick the diameter box in the calculator.
How much liquid is left in a horizontal tank?
Choose Liquid in a tank, pick horizontal cylinder, and enter the inside diameter, the length and the depth on the dipstick. The calculator shows the gallons left and how full the tank is.
How do I calculate CBM for a shipment?
Multiply length × width × height of a carton in meters, or in centimeters and divide by 1,000,000, then multiply by the number of cartons. Enter several carton sizes in the Boxes tab to add them up.
What is dimensional weight?
It is a billing weight based on size: the carton volume in cubic inches divided by 139 (or cm³ divided by 5000). Carriers charge the higher of this and the real weight.
Is volume the same as capacity?
Capacity is the volume a container can hold, usually measured with the inside dimensions and given in liters or gallons. Volume can describe a solid object too, such as a block of concrete.
How to calculate volume for any shape
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