Surface Area Calculator – Find Area of 3D Shapes
Compute surface area and volume of common 3D shapes.
About the Surface Area Calculator
What is the Surface Area Calculator?
A surface area calculator finds the surface area (and volume) of common 3D shapes: cubes, boxes, spheres, cylinders and cones.
Why use this calculator?
Painting cans, packaging, heating calculations and school geometry all need surface area, and the formulas differ per shape.
How to use it
- Choose the 3D shape.
- Enter the dimensions it needs.
- Read surface area and volume together.
Formula
Standard formulas, e.g. cylinder 2πr(r+h), sphere 4πr².
For a cone the calculator derives the slant height from radius and height automatically.
Frequently Asked Questions
Why does a sphere have the smallest surface area for volume?
Droplets and bubbles minimize surface area; the sphere is the mathematically optimal shape for containing volume.
Surface area or volume for paint?
Paint covers area, so use surface area. Volume matters for what the container holds.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Which units should I use?
Use one consistent unit for every input. The result will be in that unit (or its square or cube for area and volume).
How is area different from perimeter?
Perimeter is the distance around a shape; area is the space it covers. Perimeter is measured in units, area in square units.
Does the orientation of the shape matter?
No. Area, perimeter and volume depend only on the dimensions, not on how the shape is rotated or positioned.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.