Surface Area Calculator
Compute surface area for common 3D shapes using exact formulas and unit-consistent inputs.
7+ shapes Unit-aware Formula preview
Surface area formulas by shape
Below are the same formulas the calculator uses internally:
1. Cube
\( SA = 6a^2 \)
where \( a \) is the edge length.
2. Rectangular prism / box
\( SA = 2(lw + lh + wh) \)
where \( l \) = length, \( w \) = width, \( h \) = height.
3. Sphere
\( SA = 4 \pi r^2 \)
4. Cylinder
Closed (top + bottom): \( SA = 2\pi r^2 + 2\pi r h \)
Open-top: \( SA = \pi r^2 + 2\pi r h \)
Lateral only: \( SA = 2\pi r h \)
5. Right circular cone
\( SA = \pi r (r + s) \) where \( s = \sqrt{r^2 + h^2} \) is the slant height.
6. Square pyramid
\( SA = a^2 + 2a\ell \) where \( \ell = \sqrt{(a/2)^2 + h^2} \)
7. Right triangular prism
Triangle legs \( a \), \( b \), length \( L \):
Triangle area \( = \frac{1}{2}ab \)
Hypotenuse \( c = \sqrt{a^2 + b^2} \)
Surface area \( SA = 2 \times \frac{1}{2}ab + (a + b + c)L \)
\( SA = ab + (a + b + c)L \)
If your shape isn’t here (torus, ellipsoid, frustum…), see our dedicated geometry pages.
Example: cylinder with no top
Given: radius 3 in, height 10 in, open-top.
- Base area = \( \pi r^2 = \pi \times 3^2 = 28.274 \text{ in}^2 \)
- Lateral area = \( 2\pi r h = 2\pi \times 3 \times 10 = 188.496 \text{ in}^2 \)
- Total SA = 28.274 + 188.496 = 216.770 in²
The calculator does this for you in one click.
Surface Area Calculator – FAQ
Formula (LaTeX) + variables + units
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1. Cube \( SA = 6a^2 \) where \( a \) is the edge length.
2. Rectangular prism / box \( SA = 2(lw + lh + wh) \) where \( l \) = length, \( w \) = width, \( h \) = height.
3. Sphere \( SA = 4 \pi r^2 \)
4. Cylinder Closed (top + bottom): \( SA = 2\pi r^2 + 2\pi r h \) Open-top: \( SA = \pi r^2 + 2\pi r h \) Lateral only: \( SA = 2\pi r h \)
5. Right circular cone \( SA = \pi r (r + s) \) where \( s = \sqrt{r^2 + h^2} \) is the slant height.
6. Square pyramid \( SA = a^2 + 2a\ell \) where \( \ell = \sqrt{(a/2)^2 + h^2} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.