Surface Area Calculator
Select Solid Shape
Results
| Total Surface Area | — |
|---|---|
| Formula Used | — |
How to Use This Surface Area Calculator
Paint coverage, sheet-metal wraps, and packaging material all need the outside skin of a solid—not the air inside. Choose a shape tab, enter the labeled dimensions, and press Calculate Surface Area. The tool returns total SA and the formula string used for that solid.
- Pick a solid tab. Sphere, Cylinder, Cone, Cube, Rectangular Prism, Triangular Prism, or Pyramid.
- Fill positive dimensions. Cone and pyramid modes use vertical height h; slant lengths are computed internally.
- Press Calculate Surface Area. Results show total SA and the formula row for verification.
- Read the step block. Cylinder and cone runs split base and lateral areas before adding.
For interior cubic capacity, switch to the Volume Calculator. For flat footprints, use the Area Calculator.
Surface Area Formulas and Practical Applications
Surface area is the sum of every exposed face. The blocks below mirror the seven tabs and the JavaScript formulas on this page.
Sphere and cube
SA = 4πr²
SA = 6s²
A sphere's SA is exactly four times the area of its great circle. A cube adds six identical square faces.
Cylinder and cone
SA = 2πr² + 2πrh
SA = πr² + πrs where s = √(r² + h²)
Cylinder SA is two circular caps plus the rectangular wrap if you slit the wall flat. Cone SA adds the circular base to the sector-shaped lateral skin.
Prisms and pyramid
SA = 2(lw + lh + wh) (rectangular prism)
SA = 2 × BaseArea + P_base × L (triangular prism)
SA = s² + 2s × L_slant where L_slant = √((s/2)² + h²) (square pyramid)
The triangular prism tab accepts any valid triangle for the base—area comes from Heron's formula, not a right-angle shortcut.
Standard Units and Conversion Tables
Length inputs produce square-unit surface area. Stay in one system per run.
| Length unit | Surface area unit |
|---|---|
| Meters (m) | Square meters (m²) |
| Feet (ft) | Square feet (ft²) |
| Inches (in) | Square inches (in²) |
Browse math calculators for circle, area, and volume companions.
Frequently Asked Questions
How do you calculate the surface area of a cylinder?
SA = 2πr² + 2πrh—two bases plus lateral wrap. Enter r and vertical h on the Cylinder tab.
What is slant height in a cone?
s = √(r² + h²) along the tapered side. The tool computes it from your radius and vertical height.
Does the triangular prism tab require a right triangle?
No—any triangle obeying the side inequality works. Base area uses Heron's formula; sides must sum correctly or the tool errors.
What is the difference between surface area and volume?
Surface area is skin in square units; volume is fill in cubic units. See the Volume Calculator for capacity.
What unit is surface area reported in?
Square units of your length inputs—ft yields ft².
Disclaimer. RapidRatio is informational only—not coating spec or structural advice. Confirm material orders with qualified estimators.