Surface area is the total area of every outer face of a 3D solid — what you'd paint or wrap — measured in square units. Volume is the space inside, in cubic units. A cube is 6s², a box 2(lw + lh + wh), a sphere 4πr², a cylinder 2πr(r + h), and a cone πr(r + ℓ) with slant height ℓ. This calculator returns both surface area and volume, with the formula it used.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: standard solid-geometry formulas, recomputed in code.
Surface area & volume by solid
Each surface-area formula simply adds up the solid's faces: six squares for a cube; two circular ends plus a wrapped rectangle for a cylinder; a circular base plus a cone of slant ℓ for a cone. Volume measures the inside instead. Notice surface area always carries square units and volume cubic units, so when a shape doubles in size its surface area grows fourfold but its volume eightfold — the square-cube law.
Worked example — cube and cone
Scenario: a cube of side 3 and a cone with r = 3, h = 4.
The cube's surface area is 54 square units (six 3×3 faces) and its volume 27. For the cone, the slant height comes from the Pythagorean theorem, ℓ = 5, giving a surface area of π × 3 × 8 ≈ 75.40 and a volume of ≈ 37.70. A sphere of radius 3 has surface area and volume that both work out to ≈ 113.10 — a neat coincidence at r = 3 only.
Frequently Asked Questions
The total area of all outer faces of a 3D shape, in square units. A cube of side 3 → 6 × 9 = 54.
6s² (six square faces). s = 3 → 54, volume s³ = 27. A box is 2(lw + lh + wh); 4×3×2 → 52.
4πr², volume (4/3)πr³. r = 3 → ≈ 113.10 for both (only at r = 3).
Cylinder 2πr(r + h) → r=2,h=5 ≈ 87.96. Cone πr(r + ℓ), ℓ = √(r²+h²); r=3,h=4 → ℓ=5, ≈ 75.40.
Surface area = outside (square units, for paint/wrap); volume = inside (cubic units, for capacity). Cube 3: 54 vs 27.