About

Miscalculating volume costs money. Ordering 10m³ of concrete when you need 12 means a second delivery, pump re-hire, and a cold joint in your pour. This calculator computes volume in cubic meters for eight standard geometric solids. It accepts dimensions in any common length unit and converts internally to meters before applying the exact closed-form formula for each shape. Results are displayed in m³ alongside conversions to liters, cubic feet, cubic inches, US gallons, and imperial gallons. The tool assumes ideal geometry. Real-world objects with irregular surfaces, draft angles, or rounded fillets will deviate from these values. Always add a waste factor of 5 - 10% for construction materials.

Formulas

All shapes use closed-form volume equations. Dimensions are first converted to meters via the length-unit factor f, so that d_m = d_input × f. Volume is then computed in m³.

Rectangular Prism

V = L × W × H

Cylinder

V = π ⋅ r² ⋅ h

Sphere

V = 43 ⋅ π ⋅ r³

Cone

V = 13 ⋅ π ⋅ r² ⋅ h

Rectangular Pyramid

V = 13 ⋅ L ⋅ W ⋅ H

Hemisphere

V = 23 ⋅ π ⋅ r³

Ellipsoid

V = 43 ⋅ π ⋅ a ⋅ b ⋅ c

Triangular Prism

V = 12 ⋅ b ⋅ h_t ⋅ L

Where: L = length, W = width, H = height, r = radius, h = height, a, b, c = semi-axes of the ellipsoid, b = triangle base width, h_t = triangle height, f = unit-to-meters conversion factor. All lengths in the formulas above are assumed to be in meters after conversion.

Reference Data

Shape	Formula	Variables	Typical Use Case
Rectangular Prism (Box)	V = L × W × H	Length, Width, Height	Shipping containers, rooms, concrete slabs
Cylinder	V = π × r² × h	Radius, Height	Pipes, tanks, columns, silos
Sphere	V = 43 π r³	Radius	Balls, domes, globes
Cone	V = 13 π r² h	Radius, Height	Funnels, sand piles, hoppers
Pyramid	V = 13 L × W × H	Base Length, Base Width, Height	Roofing, aggregate stockpiles
Hemisphere	V = 23 π r³	Radius	Dome structures, bowls, tank heads
Ellipsoid	V = 43 π a b c	Semi-axes a, b, c	Pressure vessels, fuel tanks
Triangular Prism	V = 12 b × h_t × L	Base, Triangle Height, Length	A-frame roofs, troughs, wedges
Volume Unit Conversion Reference
1 m³	1000 liters = 35.3147 ft³ = 61023.7 in³
1 m³	264.172 US gal = 219.969 imp gal = 1.30795 yd³
Length Unit → Meters Factor
mm	0.001
cm	0.01
m	1
in	0.0254
ft	0.3048
yd	0.9144
km	1000

Frequently Asked Questions

Add a waste factor between 5% and 10% to the calculated volume. For concrete, 7% is standard to cover spillage, over-excavation, and form bulging. For gravel and sand, use 10% due to settling and spreading losses.

Geometric formulas assume perfect shapes. Excavations have sloped sides, tanks have weld seams and fillets, and forms may deflect. Measure the actual cross-section at multiple points and average them. For irregular shapes, break the object into simpler sub-shapes, calculate each volume separately, and sum them.

1 m³ = 1000 liters. Use cubic meters for solid materials (concrete, soil, timber) and large liquid storage. Use liters for smaller liquid quantities such as paint, fuel, or water tank capacities under 10 m³.

Liquids expand with heat. Water at 80°C occupies about 2.8% more volume than at 4°C. Gases follow the ideal gas law where volume is proportional to absolute temperature. This calculator computes geometric volume only. For precise fluid capacity at a specific temperature, apply the thermal expansion coefficient β of the substance.

Yes, by decomposition. Break the L-shape into two rectangular prisms. Calculate each separately, then add the results. For complex curved shapes, approximate using an ellipsoid or cylinder that best fits the cross-section, then verify with physical measurements.

The formula requires the radius r, which is half the diameter d. If you input the diameter where the radius is expected, your result will be 4× too large because the radius is squared in the formula. This calculator labels the field as radius. Measure carefully.