Surface Area Formulas — All 3D Shapes Reference A complete reference of surface area formulas for solid 3D shapes. Lateral surface area covers only the curved/side surfaces; total surface area also includes the base(s). Each formula links to its full page where available.
Prisms S A = 2 ( l w + l h + w h ) SA = 2(lw + lh + wh) S A = 2 ( l w + l h + w h ) Triangular Prism (base perimeter P)
S A = P ⋅ ℓ + 2 ⋅ 1 2 b h t SA = P \cdot \ell + 2 \cdot \tfrac{1}{2} b h_t S A = P ⋅ ℓ + 2 ⋅ 2 1 b h t General Right Prism (Total)
S A = 2 B + P h ( B = base area , P = base perimeter ) SA = 2 B + P h \quad(B = \text{base area},\ P = \text{base perimeter}) S A = 2 B + P h ( B = base area , P = base perimeter ) General Right Prism (Lateral)
Cylinders S A = 2 π r 2 + 2 π r h SA = 2 \pi r^2 + 2 \pi r h S A = 2 π r 2 + 2 π r h Cylinder (Lateral)
L A = 2 π r h L\!A = 2 \pi r h L A = 2 π r h Hollow Cylinder (Tube)
S A = 2 π ( R + r ) h + 2 π ( R 2 − r 2 ) SA = 2\pi (R + r) h + 2\pi(R^2 - r^2) S A = 2 π ( R + r ) h + 2 π ( R 2 − r 2 ) Pyramids & Cones Square Pyramid (Total)
S A = s 2 + 2 s ℓ ( ℓ = slant height ) SA = s^2 + 2 s \ell \quad(\ell = \text{slant height}) S A = s 2 + 2 s ℓ ( ℓ = slant height ) Regular Pyramid (Total)
S A = B + 1 2 P ℓ SA = B + \tfrac{1}{2} P \ell S A = B + 2 1 P ℓ Regular Pyramid (Lateral)
L A = 1 2 P ℓ L\!A = \tfrac{1}{2} P \ell L A = 2 1 P ℓ S A = π r 2 + π r ℓ SA = \pi r^2 + \pi r \ell S A = π r 2 + π r ℓ Cone (Lateral)
L A = π r ℓ L\!A = \pi r \ell L A = π r ℓ Conical Frustum (Lateral)
L A = π ( R + r ) ℓ L\!A = \pi (R + r) \ell L A = π ( R + r ) ℓ Spheres & Curved Solids S A = 4 π r 2 SA = 4 \pi r^2 S A = 4 π r 2 Hemisphere (Total)
S A = 3 π r 2 SA = 3 \pi r^2 S A = 3 π r 2 Hemisphere (Curved Only)
S A = 2 π r 2 SA = 2 \pi r^2 S A = 2 π r 2 Spherical Cap (height h)
S A = 2 π r h SA = 2 \pi r h S A = 2 π r h Torus
S A = 4 π 2 R r SA = 4 \pi^2 R r S A = 4 π 2 R r Ellipsoid (approx.)
S A ≈ 4 π ( a p b p + a p c p + b p c p 3 ) 1 / p , p = 1.6075 SA \approx 4\pi \left(\tfrac{a^p b^p + a^p c^p + b^p c^p}{3}\right)^{1/p},\ p = 1.6075 S A ≈ 4 π ( 3 a p b p + a p c p + b p c p ) 1/ p , p = 1.6075 Calculus: Surface Area by Integration Surface of Revolution about x-axis
S A = 2 π ∫ a b y 1 + ( d y d x ) 2 d x SA = 2 \pi \int_a^b y\,\sqrt{1 + \left(\tfrac{dy}{dx}\right)^2}\,dx S A = 2 π ∫ a b y 1 + ( d x d y ) 2 d x Surface of Revolution about y-axis
S A = 2 π ∫ a b x 1 + ( d x d y ) 2 d y SA = 2 \pi \int_a^b x\,\sqrt{1 + \left(\tfrac{dx}{dy}\right)^2}\,dy S A = 2 π ∫ a b x 1 + ( d y d x ) 2 d y Parametric Surface of Revolution
S A = 2 π ∫ a b y ( t ) ( x ′ ( t ) ) 2 + ( y ′ ( t ) ) 2 d t SA = 2 \pi \int_a^b y(t)\,\sqrt{(x'(t))^2 + (y'(t))^2}\,dt S A = 2 π ∫ a b y ( t ) ( x ′ ( t ) ) 2 + ( y ′ ( t ) ) 2 d t 