Volume Calculatorv1.0.0

Enter shape dimensions, choose units, and compute volume instantly. Provide values as fractions (e.g., 3/4), decimals (e.g., 0.75), or percentages (e.g., 75%). Adjust π when needed, select output units, and compare scenarios by changing inputs.

• Select a shape from the “Calculate the Volume of a” menu.
• Enter the required dimensions in the inputs that appear. The calculator normalizes fractions and percentages on blur.
• Set π if the shape requires it (default is 3.141592653589793). Shapes that use π include: capsule, cone, conical frustum, cylinder, ellipsoid, hemisphere, sphere, spherical cap, and tube.
• Choose Units. For length units (m, cm, in, etc.), the result appears as cubic units (e.g., m³). For liters, enter dimensions in centimeters; for gallons, enter dimensions in inches. The tool converts cm³ to liters (1,000 cm³ = 1 L) and in³ to US gallons (231 in³ = 1 gal).
• Click Calculate to view the volume. Review the live result below the buttons.
• Click Reset to restore defaults and clear saved state.

Use the query string to prefill inputs (e.g., ?shape=cylinder&r=2&h=5&units=cm). The calculator autosaves your last state in the browser and recalculates as you edit fields.

Use the following plain-text formulas to verify results or copy into your 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

Confirm units before calculating. Length units output in cubic length units. Liters assume inputs in centimeters (cm³ ÷ 1,000). Gallons assume inputs in inches (in³ ÷ 231).

Apply the calculator to plan projects, verify homework, and estimate materials. Use precise inputs and unit conversions to improve 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.