Result
Result reflects the current submitted inputs.
- Risk A
- Reviewed 2026-05-26
- 1 sources
- Inputs use one consistent linear unit.
- Surface area is reported in square units.
- Intermediate values are not rounded.
- Box surface area uses 2 x (length x width + length x height + width x height).
Accuracy notes
- Risk level
- A
- Reviewed
- 2026-05-26
- Sources
- 1
- Primary result
- Surface area
Formula logic is kept in a pure calculator module with fixtures, source notes, and page-visible assumptions.
What the result means
Surface area is the total exterior area of the shape. Use it to estimate paint coverage, wrapping material, or any quantity that scales with exposed surface.
Use the result this way
- Start with Surface area, then use supporting outputs for context.
- Verify Shape, Length, and Width before copying the result.
- Check the formula, example, and assumptions before reusing the answer.
User job
How to use this calculator
Use Surface Area Calculator when you need surface area for quick number work, classwork, spreadsheet checks, and explaining a calculation to someone else.
Best for
- Checking the core numeric relationship
- Comparing the main result with supporting outputs
- Reviewing a default example before entering your own shape and length.
Check before relying
- Confirm sign, decimal, percent, and rounding assumptions before copying the number.
- Inputs use one consistent linear unit.
- The cylinder is a closed right circular cylinder.
- Source context: OpenStax, reviewed 2026-06-18.
Next useful step
- Volume CalculatorUse next when your task shifts from Surface Area Calculator to Volume Calculator.
- Area CalculatorUse next when your task shifts from Surface Area Calculator to Area Calculator.
- Square Footage CalculatorUse next when your task shifts from Surface Area Calculator to Square Footage Calculator.
Formula
Cube: SA = 6 x s^2. Rectangular prism: SA = 2(lw + lh + wh). Cylinder: SA = 2 x pi x r^2 + 2 x pi x r x h. Sphere: SA = 4 x pi x r^2. Cone: SA = pi x r^2 + pi x r x l (where l is slant height). Always square the units.
- Cube: 6 x side^2 (six identical square faces).
- Rectangular prism: SA = 2(lw + lh + wh) — three pairs of identical faces.
- Cylinder: 2 caps (2 x pi x r^2) plus the side (2 x pi x r x h).
- Sphere: SA = 4 x pi x r^2 — exactly 4 times the area of a great circle.
- Cone: base (pi x r^2) plus lateral (pi x r x l), where l is the slant height; slant = sqrt(r^2 + h^2).
Inputs
Choose the shape, enter the dimensions. The calculator sums all face areas (or uses the closed formula) and returns total surface area in square units of whatever length you used.
Example
Cube with side 4: SA = 6 x 16 = 96 cm^2. Cylinder r=3, h=7: SA = 2 x pi x 9 + 2 x pi x 3 x 7 = pi x (18 + 42) = about 188.50. Sphere r=5: SA = 4 x pi x 25 = about 314.16.
FAQ
What is surface area?
Surface area is the total area of all the outer faces of a 3D shape, measured in square units. It tells you how much paint, wrap, or material is needed to cover the exterior.
How do you calculate the surface area of a cube?
Multiply the side length squared by 6: SA = 6 x s^2. A cube with side 4 has surface area 6 x 16 = 96 square units.
What is the surface area formula for a cylinder?
SA = 2 x pi x r^2 + 2 x pi x r x h. The first term is the two circular caps, the second is the curved side unrolled into a rectangle of width 2 x pi x r and height h.
What is the surface area of a sphere?
SA = 4 x pi x r^2. For r = 5, SA = 4 x pi x 25, about 314.16 square units.
How is surface area different from volume?
Surface area measures the outside (in square units), volume measures the inside (in cubic units). Two shapes with the same volume can have very different surface areas.
What should I verify before using surface area calculator?
Verify shape, length, and width, the displayed formula, and the worked example before copying the result into another document or decision.
Sources
Last reviewed: 2026-05-26
- academicReviewed 2026-06-18Prealgebra 2e, Section 9.6: Volume and Surface AreaOpenStax. Surface area formulas for common 3D shapes.
Disclaimer
Results assume a perfect geometric shape with the dimensions entered. Real surfaces may have features (handles, holes, texture) that change effective area.