Volume Calculator

The volume calculator computes the volume of 13 solid shapes, sphere, hemisphere, ellipsoid, cylinder, cone, conical frustum, capsule, tube, spherical cap, cube, rectangular prism, triangular prism, and square pyramid, from their dimensions. Values can be entered as fractions (for example, 3/4), decimals (for example, 0.75), or percentages (for example, 75%), and π can be adjusted from its default of 3.141592653589793 when the shape requires it.

• Dimensions accept fractions and percentages directly; they normalize to a decimal value automatically.
• π applies to shapes built from circular or spherical cross-sections: capsule, cone, conical frustum, cylinder, ellipsoid, hemisphere, sphere, spherical cap, and tube.
• Length units such as m, cm, or in return a cubic-unit result, such as m³. Liters and gallons are volume-direct options instead: liters assume dimensions entered in centimeters, converting at 1,000 cm³ per liter, and gallons assume dimensions in inches, converting at 231 in³ per US gallon.

Inputs autosave in the browser and the result recalculates as values change.

The plain-text formulas behind each shape, useful for verifying a result or copying into notes:

• Cube: V = a³
• Rectangular Prism: V = h × w × l
• Sphere: V = (4/3) × π × r³
• Hemisphere: V = (2/3) × π × r³
• Cylinder: V = π × r² × h
• Cone: V = (1/3) × π × r² × h
• Conical Frustum: V = (1/3) × π × h × (r₁² + r₂² + r₁ × r₂)
• Square Pyramid: V = (1/3) × a² × h
• Triangular Prism (Heron for base): let s = (a + b + c) / 2, A = √[s(s − a)(s − b)(s − c)], then V = A × h
• Ellipsoid: V = (4/3) × π × a × b × c
• Spherical Cap: V = (1/3) × π × h² × (3r − h)
• Capsule (cylinder with hemispherical ends): V = π × r² × a + (4/3) × π × r³
• Tube (hollow cylinder): V = π × (r₁² − r₂²) × l

Units matter before reading a result: length units output in cubic length units, liters assume input in centimeters (cm³ ÷ 1,000), and gallons assume input in inches (in³ ÷ 231).

A cylinder with radius 2 and height 5 has volume V = π × r² × h = π × 4 × 5 = 20π, approximately 62.83 cubic units. At the default π (3.141592653589793), that rounds to 62.8319.

Volume calculations plan projects, verify homework, and estimate materials, with precise inputs and unit conversions improving accuracy.

• Construction and DIY: Estimate concrete for footings, volume of backfill, or capacity of planters and tanks.
• Engineering and Fabrication: Size enclosures, reservoirs, and pipes; compare designs by testing shape parameters.
• Education and Tutoring: Check geometry assignments, demonstrate formula application, and explore unit conversions.
• Manufacturing and Materials: Calculate resin, metal, or plastic requirements for parts with common profiles.
• Science and Lab Work: Determine container volumes, spherical or ellipsoidal sample volumes, and displacement estimates.
• Logistics and Storage: Compute capacity of bins, drums, and silos to plan inventory and space usage.
• Aquariums and Gardening: Convert tank and planter dimensions to liters or gallons for stocking or watering plans.

Improve results by matching input units to the selected output unit system, verifying π where high precision is required, and testing multiple scenarios to understand sensitivity to dimension changes.