Education
Volume Calculator
Pick a shape, enter the required dimensions in any common unit, and the calculator returns the volume in your chosen cubic unit, the equivalent in cubic feet and cubic yards, and the formula it used.
Shape
Measurement unit
Switch the shape to update the inputs. All dimensions use the same unit; results show the equivalent volume in cubic feet and cubic yards.
Volume
480 ft³
V = L × W × H
Volume of a rectangular prism with length 10 feet, width 8 feet, and height 6 feet is 480 ft³.
Examples
Box 10 × 8 × 6 ft
= 480 ft³
Cube with side 5 ft
= 125 ft³
Cylinder r=5 ft, h=10 ft
≈ 785.40 ft³
Sphere r=5 in
≈ 523.60 in³
How it works
Volume is the amount of 3D space inside a solid. The formula depends on the shape, but the calculator runs the right one for the shape you pick.
Rectangular prism
V = L × W × H
Cube
V = s³
Cylinder
V = π × r² × h
Sphere
V = (4/3) × π × r³
Cone
V = (1/3) × π × r² × h
Pyramid (rectangular base)
V = (1/3) × base length × base width × h
All dimensions use the same unit. The calculator returns the volume in your chosen cubic unit and the equivalent in cubic feet, cubic yards, and cubic meters using fixed conversion factors.
What is a volume calculator?
A volume calculator computes how much 3D space a solid shape takes up. Pick the shape, enter the required dimensions in any common unit, and the calculator runs the right formula and returns the volume in cubic units. This calculator covers the six shapes you meet most often in geometry class and in everyday measurement: rectangular prism, cube, cylinder, sphere, cone, and pyramid.
How the volume calculator works
Pick a shape, enter the dimensions, and the calculator:
- Applies the volume formula for the chosen shape.
- Reports the volume in the cubic unit that matches your input (in³, ft³, yd³, cm³, or m³).
- Converts the result to cubic feet, cubic yards, and cubic meters using fixed factors.
- Shows the formula it used and a short plain English explanation.
Volume formulas for common shapes
- Rectangular prism: V = L × W × H
- Cube: V = s³
- Cylinder: V = π × r² × h
- Sphere: V = (4/3) × π × r³
- Cone: V = (1/3) × π × r² × h
- Pyramid (rectangular base): V = (1/3) × base length × base width × h
All formulas multiply three dimensions, so the result is always in cubic units. The radius r in the cylinder, sphere, and cone formulas is half the diameter of the circular base or sphere.
Cubic unit conversions
- 1 cubic foot = 1,728 cubic inches
- 1 cubic yard = 27 cubic feet
- 1 cubic meter ≈ 35.31 cubic feet
- 1 cubic meter = 1,000,000 cubic centimeters
- 1 cubic foot ≈ 0.0283 cubic meters
The calculator runs these conversions for every result, so you can switch units without having to redo the math.
Volume vs other project calculators
The volume calculator is the right tool for general 3D shape volume in any unit. For specific project workflows, dedicated calculators add the extras you actually need when ordering materials:
- The cubic feet calculator focuses on box-shaped volumes (storage, shipping, refrigerators) in cubic feet first.
- The cubic yard calculator focuses on landscaping and concrete volumes in cubic yards, with weight estimates.
- The concrete calculator adds the number of bags or yards of mixed concrete you need for slabs, footings, and columns.
- The gravel calculator converts cubic yards of gravel into tons for delivery.
- The square footage calculator covers 2D area (floors, walls, yards), not 3D volume.
Use the volume calculator on this page for the pure math of any 3D shape; use the project calculators when you also need bags, tons, or area-specific output.
Worked examples
- Box 10 × 8 × 6 ft: V = 10 × 8 × 6 = 480 cubic feet.
- Cube with side 5 ft: V = 5³ = 125 cubic feet.
- Cylinder r = 5 ft, h = 10 ft: V = π × 25 × 10 ≈ 785.40 cubic feet.
- Sphere r = 5 in: V = (4/3) × π × 125 ≈ 523.60 cubic inches.
- Cone r = 5 ft, h = 10 ft: V = (1/3) × π × 25 × 10 ≈ 261.80 cubic feet.
- Pyramid 6 × 4 × 9 ft: V = (1/3) × 6 × 4 × 9 = 72 cubic feet.
Common mistakes
- Using diameter where the formula calls for radius. The cylinder, sphere, and cone formulas use radius, which is half the diameter.
- Forgetting the 1/3 factor on cones and pyramids. A cone or pyramid holds exactly one third of the cylinder or prism with the same base and height.
- Mixing units within a single calculation. All dimensions must use the same unit before multiplying.
- Confusing area with volume. Area is 2D and uses square units; volume is 3D and uses cubic units.
- Treating diameter as the base width for a pyramid. The pyramid formula uses base length and base width, not radius.
Related tools
- Cubic feet calculator for box volume in cubic feet first.
- Cubic yard calculator for landscaping and concrete volumes.
- Square footage calculator for floor and wall area.
- Concrete calculator for slab, footing, and column estimates with bag counts.
- Gravel calculator for cubic yards and tons of gravel.
- All education calculators and all home calculators.
Note. Results are computed in standard floating-point precision and rounded for display. Volume always uses cubic units and is always 0 or positive; negative dimensions are flagged and zero dimensions return a volume of 0 with an explanation.
Frequently asked questions
Volume is the amount of 3D space a solid takes up, measured in cubic units. A cubic foot is the space inside a cube that is 1 foot on each side. Volume always uses cubic units (in³, ft³, yd³, cm³, m³) because three dimensions are multiplied together.
The formula depends on the shape. A rectangular prism uses V = length × width × height. A cube uses V = s³. A cylinder uses V = π × r² × h. A sphere uses V = 4/3 × π × r³. A cone uses V = 1/3 × π × r² × h. A pyramid uses V = 1/3 × base length × base width × height.
V = L × W × H. Multiply the length, width, and height. A box that is 10 ft × 8 ft × 6 ft has a volume of 480 cubic feet. Every face is a rectangle, and opposite faces are equal.
V = π × r² × h. Multiply pi times the radius squared times the height. The radius is half the diameter of the circular base. A cylinder with radius 5 ft and height 10 ft has a volume of about 785.4 cubic feet.
V = (4/3) × π × r³. A sphere with radius 5 inches has a volume of about 523.6 cubic inches. Radius is half the diameter.
V = (1/3) × π × r² × h. The 1/3 factor reflects the fact that a cone fills exactly one third of the cylinder it fits inside. A cone with radius 5 ft and height 10 ft has a volume of about 261.8 cubic feet.
For a rectangular-base pyramid, V = (1/3) × base length × base width × height. The 1/3 factor mirrors the cone case: a pyramid fills one third of the prism with the same base and height. For non-rectangular bases, use V = (1/3) × base area × height.
Use fixed conversion factors. 1 cubic foot = 1,728 cubic inches = 0.037 cubic yards ≈ 0.0283 cubic meters. 1 cubic yard = 27 cubic feet. 1 cubic meter ≈ 35.31 cubic feet. The calculator runs these conversions whenever you change the unit.
The volume calculator handles general 3D shape volume (rectangular prism, cube, cylinder, sphere, cone, pyramid) and reports the volume in any of several cubic units. The cubic feet and cubic yards calculators focus on box-shaped volumes for shipping and storage; the concrete and gravel calculators add bag and tonnage estimates for specific project materials. Pick the dedicated tool when you need its specialty math.
No. Volume is a measure of physical space, so it is always 0 or positive. Negative dimensions are not allowed, and a 0 dimension collapses the shape and produces a volume of 0.
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