Math
Surface Area Calculator
The surface area calculator adds up every face of a solid — the curved side of a cylinder, the four triangular faces of a pyramid, the two ends of a prism — and shows the formula it used.
Pick a solid, enter its dimensions, and get the total surface area in square units alongside the lateral (side-only) area and the volume.
Surface area is reported in square units of this.
Perpendicular height (not the slant).
Half the diameter.
Try an example
Result
Total surface area
—
- Total surface area (with units)
- —
- Lateral area (sides only)
- —
- Base area(s)
- —
- Volume
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- Formula
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Study path
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What the surface area calculator solves
The surface area calculator adds up every face of a solid — the curved side of a cylinder, the four triangular faces of a pyramid, the two ends of a prism — and shows the formula it used. Pick a solid, enter its dimensions, and get the total surface area in square units alongside the lateral (side-only) area and the volume.
Formula
How to use it
- Choose the solid.
- Enter its dimensions in one unit (use the vertical height, never a slant) and pick the unit.
- Read the total surface area, the lateral part, the base part, and the volume for comparison.
How to read the answer
Surface area is the total area of all the outside faces, so it is measured in square units. The lateral area is the sides only (a label around a can, the walls of a box); adding the top and bottom gives the total. Round solids keep an exact π form when the dimensions are simple.
Common mistakes and edge cases
- Using the slant height where the formula needs the vertical height, or vice versa. Cones and pyramids need the slant for the faces; the calculator derives it from the height.
- Leaving out one of the two ends of a cylinder or prism.
- Reporting cubic units — surface area is always square units; the volume line is there for comparison.
- A dimension of zero or less cannot form a solid and is rejected.
Worked examples
Cylinder r = 3, h = 4 (42π)
Total surface area
131.9469
Cube edge 4
Total surface area
96
Box 10 × 6 × 4
Total surface area
248
Cone r = 3, h = 4 (24π)
Total surface area
75.3982
Sphere r = 3 (36π)
Total surface area
113.0973
Square pyramid 6 × 6 base, height 4
Total surface area
96
Triangular prism 3-4-5, length 10
Total surface area
132
Decimal box 2.5 × 1.5 × 0.5
Total surface area
11.5
Zero radius sphere (impossible)
Total surface area
Error
Frequently asked questions
What is the surface area of a cylinder?+
SA = 2πrh + 2πr²: the curved side (a rectangle 2πr wide and h tall) plus two circular ends. Radius 3 and height 4 give 42π ≈ 131.95.
What is the surface area of a rectangular prism?+
SA = 2(lw + lh + wh) — each of the three distinct faces appears twice. A 10 × 6 × 4 box has surface area 248.
What is lateral surface area?+
The area of the sides only, without the top and bottom. For a cylinder it is 2πrh; for a box it is the perimeter of the base times the height.
How do I find the surface area of a cone?+
SA = πrl + πr², where l = sqrt(r² + h²) is the slant height. With r = 3 and h = 4, l = 5 and SA = 15π + 9π = 24π.
How is the surface area of a pyramid calculated?+
Base area plus the triangular faces. For a rectangular base each pair of opposite faces has its own slant height: sqrt(h² + (w/2)²) for the faces along the length and sqrt(h² + (l/2)²) for the faces along the width.
Why is surface area in square units when volume is in cubic units?+
Surface area measures a 2D skin (length × length); volume measures 3D space (length × length × length). A 4 cm cube has surface area 96 cm² and volume 64 cm³.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026