Volume Calculator
Compute volume for common 3D shapes from dimensions.
1. Select shape & unit
2. Enter dimensions
All dimensions must use the same unit you selected above.
3. Result
Volume: —
Shown in cubic cm. Make sure all inputs use the same unit.
Liters: — | US gal: —
Formula
V = l × w × h
Volume: recap
In solid geometry, volume measures the space a 3D object occupies. For regular solids, we have closed-form formulas; for irregular objects we normally have to integrate or approximate.
Most used formulas
- Cube: \( V = a^3 \)
- Rectangular prism: \( V = lwh \)
- Cylinder: \( V = \pi r^2 h \)
- Cone: \( V = \frac{1}{3} \pi r^2 h \)
- Sphere: \( V = \frac{4}{3} \pi r^3 \)
- Square pyramid: \( V = \frac{1}{3} b^2 h \)
- Triangular prism: \( V = \frac{1}{2} b h_t \cdot L \)
- Torus: \( V = 2 \pi^2 R r^2 \)
Units & conversions
1 dm³ = 1 L, 1 m³ = 1000 L, 1 US gallon ≈ 3.78541 L. So once you get the volume in cubic cm (cm³), divide by 1000 to get liters.
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
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Variables and units
- No variables provided in audit spec.
Sources (authoritative):
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.