Volume Formulas — All 3D Shapes Reference A complete reference of volume formulas for solid 3D shapes. Covers prisms, pyramids, cylinders, cones, spheres, and special solids. Each formula links to its full page where available.
Prisms General Prism
V = B ⋅ h ( B = base area ) V = B \cdot h \quad(B = \text{base area}) V = B ⋅ h ( B = base area ) Triangular Prism
V = 1 2 b h ⋅ ℓ V = \tfrac{1}{2} b h \cdot \ell V = 2 1 bh ⋅ ℓ Hexagonal Prism
V = 3 3 2 s 2 ⋅ h V = \tfrac{3\sqrt{3}}{2} s^2 \cdot h V = 2 3 3 s 2 ⋅ h Oblique Prism
V = B ⋅ h ⊥ ( h ⊥ = perpendicular height ) V = B \cdot h_\perp \quad(h_\perp = \text{perpendicular height}) V = B ⋅ h ⊥ ( h ⊥ = perpendicular height ) Pyramids V = 1 3 B h V = \tfrac{1}{3} B h V = 3 1 B h Square Pyramid
V = 1 3 s 2 h V = \tfrac{1}{3} s^2 h V = 3 1 s 2 h Rectangular Pyramid
V = 1 3 l w h V = \tfrac{1}{3} l w h V = 3 1 l w h Triangular Pyramid (Tetrahedron, regular)
V = 2 12 s 3 V = \tfrac{\sqrt{2}}{12} s^3 V = 12 2 s 3 Pyramidal Frustum
V = h 3 ( B 1 + B 2 + B 1 B 2 ) V = \tfrac{h}{3}\left(B_1 + B_2 + \sqrt{B_1 B_2}\right) V = 3 h ( B 1 + B 2 + B 1 B 2 ) Cylinders & Cones V = π r 2 h V = \pi r^2 h V = π r 2 h Oblique Cylinder
V = π r 2 h ⊥ V = \pi r^2 h_\perp V = π r 2 h ⊥ Hollow Cylinder (Tube)
V = π ( R 2 − r 2 ) h V = \pi (R^2 - r^2) h V = π ( R 2 − r 2 ) h V = 1 3 π r 2 h V = \tfrac{1}{3} \pi r^2 h V = 3 1 π r 2 h Conical Frustum
V = π h 3 ( R 2 + R r + r 2 ) V = \tfrac{\pi h}{3}\,(R^2 + R r + r^2) V = 3 π h ( R 2 + R r + r 2 ) Spheres & Curved Solids V = 4 3 π r 3 V = \tfrac{4}{3} \pi r^3 V = 3 4 π r 3 Hemisphere
V = 2 3 π r 3 V = \tfrac{2}{3} \pi r^3 V = 3 2 π r 3 Spherical Cap (height h)
V = π h 2 3 ( 3 r − h ) V = \tfrac{\pi h^2}{3}(3r - h) V = 3 π h 2 ( 3 r − h ) Ellipsoid
V = 4 3 π a b c V = \tfrac{4}{3} \pi a b c V = 3 4 π ab c Torus
V = 2 π 2 R r 2 V = 2 \pi^2 R r^2 V = 2 π 2 R r 2 Calculus: Volume by Integration Disk Method
V = π ∫ a b [ f ( x ) ] 2 d x V = \pi \int_a^b [f(x)]^2\,dx V = π ∫ a b [ f ( x ) ] 2 d x Washer Method
V = π ∫ a b ( [ R ( x ) ] 2 − [ r ( x ) ] 2 ) d x V = \pi \int_a^b \left([R(x)]^2 - [r(x)]^2\right) dx V = π ∫ a b ( [ R ( x ) ] 2 − [ r ( x ) ] 2 ) d x Shell Method
V = 2 π ∫ a b x f ( x ) d x V = 2\pi \int_a^b x\, f(x)\,dx V = 2 π ∫ a b x f ( x ) d x Known Cross-Sections
V = ∫ a b A ( x ) d x V = \int_a^b A(x)\,dx V = ∫ a b A ( x ) d x 