3D Geometric Shapes Volume Calculators

V = π × r² × h

Calculate cylinder volume from radius or diameter and height. See liters, gallons, surface area, and step-by-step math with custom units.

V = (1/3) × π × r² × h

Calculate cone volume from radius and height or slant height. See liters, gallons, step-by-step math, and equivalent cylinder comparisons.

V = (4/3) × π × r³

Calculate sphere volume from radius, diameter, or circumference tape measurement. See liters, gallons, surface area, and step-by-step math.

V = L × W × H

Calculate rectangular prism and box volume from length, width, and height. Supports mixed units per field, cubic feet, gallons, and steps.

V = s³

Calculate cube volume from edge length or find side length from volume. Includes scaling law reference, surface area, and step-by-step math.

V = (1/3) × A_base × h

Calculate pyramid volume for square, rectangular, triangular, and regular polygon bases. Features step-by-step formulas and prism comparisons.

V = (1/2) × b × h_triangle × L

Calculate triangular prism volume using base & height or 3 edge lengths with Heron’s formula. Ideal for ramps, wedges, and roof attics.

V = (2/3) × π × r³

Calculate hemisphere volume from radius or diameter. See capacity in liters, US gallons, and cups. Perfect for domes, bowls, and tanks.

V = π × r² × a + (4/3) × π × r³

Calculate capsule volume from radius and cylinder or overall length. Perfect for horizontal propane tanks, pressure vessels, and pills.

V = (1/3) × π × h × (R² + r² + R × r)

Calculate truncated cone frustum volume from top & bottom radii or diameters and height. Perfect for buckets, pots, planters, and lampshades.

V = (4/3) × π × a × b × c

Calculate ellipsoid volume from three semi-axes (a, b, c) or full diameters. Includes surface area approximation and step-by-step math.

V = 2 × π² × R × r²

Calculate torus volume and surface area from major radius (R) and minor tube radius (r). Sized for O-rings, donuts, and toroidal tanks.