Surface Area Calculator
Calculate the total surface area of a cube, rectangular prism, cylinder, or sphere from its dimensions, with the exact formula used shown alongside the result.
Calculator Inputs
Choose the 3D shape to calculate surface area for. Which dimension fields below are used — and what each one means — depends on this choice.
Cube: side length. Rectangular Prism: length. Cylinder: radius. Sphere: radius. Must be greater than 0.
Rectangular Prism: width. Cylinder: height. Not used for Cube or Sphere — ignored for those shapes regardless of value.
Rectangular Prism: height. Not used for Cube, Cylinder, or Sphere — ignored for those shapes regardless of value.
- Surface Area
- 54.00
- Shape / Formula Used
- Cube: SA = 6s² = 6 × 3²
About these results
CalcSpectrum calculators produce automated estimates using established formulas and the specific values you enter. Because real-world outcomes depend on input accuracy, mathematical assumptions, and rounding conventions, please verify critical figures with an appropriately qualified financial, tax, medical, legal, or other professional, as relevant.
How It's Calculated
Formula
This calculator computes the total exterior surface area of four common 3D shapes: a cube, a rectangular prism, a cylinder, or a sphere. Pick a shape first — that choice determines which of the three dimension fields below are actually used and what each one means. A cube needs only its side length (s) and uses SA = 6s². A rectangular prism needs all three dimensions — length (l), width (w), and height (h) — and uses SA = 2(lw + lh + wh), summing the area of all six faces. A cylinder needs a radius (r) and a height (h) and uses SA = 2πr(r + h), combining the two circular ends with the curved side. A sphere needs only a radius (r) and uses SA = 4πr². Any dimension field not needed by the shape you've selected is ignored, no matter what value sits in it. Every dimension that IS relevant to your selected shape must be greater than 0 — a zero or negative relevant dimension isn't a real measurement and is rejected rather than silently producing an invalid surface area.
Worked Examples
Cube with side length 3
- SA = 6s² = 6 × 3²
- SA = 6 × 9 = 54 square units
Cylinder with radius 2 and height 5
- SA = 2πr(r + h) = 2π × 2 × (2 + 5)
- SA = 2π × 2 × 7 ≈ 87.96 square units
Frequently Asked Questions
What's the difference between surface area and volume?
Surface area measures the total area of a shape's exterior faces (a 2D measurement, in square units) — it tells you how much material would cover the outside. Volume measures how much space the shape occupies inside (a 3D measurement, in cubic units). They use related but different formulas and are not interchangeable.
Why are some dimension fields ignored for certain shapes?
Each shape only needs a specific number of measurements: a cube and sphere each need just one (side or radius), a cylinder needs two (radius and height), and a rectangular prism needs all three (length, width, height). The extra 'Dimension' fields are shown for every shape for a consistent layout, but any field a shape doesn't use is ignored regardless of what value is in it.
Why must every relevant dimension be greater than 0?
A side length, radius, or height of zero or less doesn't correspond to a real physical shape, and would either produce a meaningless zero result or an invalid formula input. This calculator rejects those values instead of returning a misleading answer.
What units does the result use?
The result is in whatever squared unit matches your input dimensions — if you enter dimensions in centimeters, the surface area is in square centimeters; in inches, square inches; and so on. The calculator itself is unit-agnostic.