Surface Area Calculator
Cube, Prism, Sphere, Cylinder & Cone
Choose a 3D shape, enter its dimensions, and calculate its total surface area.
Understanding Surface Area
Surface area tells you how much material it would take to completely cover a three-dimensional shape — from wrapping a gift box to painting a storage tank.
This calculator covers the cube, rectangular prism (box), sphere, cylinder, and cone — the five 3D shapes you'll encounter most often in geometry, packaging, and construction.
Because surface area measures a two-dimensional covering, results are always expressed in square units (in², cm², m², and so on) — never linear or cubic units.
The Five Formulas
Cube
Rectangular Prism
Sphere
Cylinder
Cone
Why the Cone Formula Looks Different
Every other shape here is built from flat faces or a simple curved band, but a cone tapers to a point. Its lateral (side) surface unrolls flat into a circular sector whose radius is the slant height (ℓ) — the distance along the cone's surface from the base edge to the apex — not the vertical height (h). Because r, h, and ℓ form a right triangle, the calculator derives the slant height automatically using the Pythagorean theorem before finishing the surface area calculation.
Cube, rectangular prism, sphere, cylinder, and cone.
Surface area covers a solid's exterior, not the space it occupies.
Spheres, cylinders, and cones all rely on π for their curved faces.
Key Takeaways
- Surface area is always in square units — it measures a covering, not a volume.
- A cone needs its slant height, not its vertical height, to find the lateral surface area — the calculator derives it for you.
- Need the space inside instead? Use the companion Volume Calculator for the same five shapes.
Frequently Asked Questions
- Choose a shape from the dropdown — Cube, Rectangular Prism, Sphere, Cylinder, or Cone.
- Enter the required dimensions for that shape (all values must be positive numbers).
- Click "Calculate" to see the total surface area.
Surface area is the total area covering the outside of a 3D (three-dimensional) solid, measured in square units. It's the sum of the areas of every face or curved surface that makes up the shape's exterior — think of it as how much wrapping paper you would need to cover the object completely, with no overlap.
Surface area measures the two-dimensional "skin" around a solid (in square units, like cm²), while volume measures the three-dimensional space it occupies inside (in cubic units, like cm³). A shape can have a large volume but a relatively small surface area, or vice versa. Use our Volume Calculator to find how much space a shape holds instead of how much surface covers it.
A cone's curved (lateral) surface unrolls into a flat sector of a circle whose radius equals the cone's slant height — the straight-line distance from the base edge up to the apex. Since the slant height, the cone's radius, and its vertical height form a right triangle, the calculator finds it automatically with slant = √(r² + h²), the same relationship used in the Pythagorean Theorem Calculator.
No — this calculator is unit-agnostic. Enter all dimensions for a single calculation in the same unit (all in centimeters, all in inches, etc.), and the result will be in that unit squared. Mixing units within one calculation will give an incorrect result.
Unlike a cube, where every edge is identical, a rectangular prism (box) can have three independent dimensions — length, width, and height — so each of its three pairs of opposite faces can have a different area. The calculator sums all six faces: two of l×w, two of l×h, and two of w×h.