Total Surface Area of 3D Solids
This surface area calculator adds up every outer face of a 3D solid and returns the total in square units. Choose a shape, type in its dimensions, and the total surface area updates instantly for seven common solids — cube, cuboid, sphere, cylinder, cone, square pyramid, and triangular prism.
Solids You Can Measure
Boxes
Round Solids
Pyramid & Prism
How to Calculate Surface Area
Pick the 3D Shape
Select the solid you want to measure. The input fields change to ask only for the dimensions that shape needs.
Enter the Dimensions
Type the side, radius, height, or base values the shape needs to describe all of its faces.
Read the Result Instantly
Total surface area is computed in real time, with the formula and a step-by-step substitution shown right below it.
Switch Units If Needed
Pick mm, cm, m, in, or ft from the dropdown, and the result label switches to the matching square unit.
Surface Area Formulas by Shape
Each solid uses a standard total surface area formula that covers all of its faces. The calculator applies the right one automatically; the full set is listed here for reference.
| Shape | Formula | Inputs Needed |
|---|---|---|
| Cube | S = 6 × a² | side a |
| Cuboid | S = 2 × (lw + lh + wh) | length l, width w, height h |
| Sphere | S = 4 × π × r² | radius r |
| Cylinder | S = 2πr(r + h) | radius r, height h |
| Cone | S = πr(r + √(r² + h²)) | radius r, height h |
| Square Pyramid | S = a² + 2a × √(a²/4 + h²) | base side a, height h |
| Triangular Prism | S = bh + l(a + b + c) | base b, tri height h, length l, sides a, c |
Features
Seven 3D Shapes
Cube, cuboid, sphere, cylinder, cone, square pyramid, and triangular prism, all in one place.
Real-Time Results
The surface area recalculates the instant you edit any value — there is no submit button.
Formula & Steps
Every answer shows its formula plus a step-by-step substitution, so you can follow the math.
Multiple Units
Work in mm, cm, m, in, or ft, with the result shown in the matching square unit.
Base & Lateral Faces
Formulas include both the base(s) and the lateral surface for a complete total surface area.
Shape Preview
An on-screen diagram shows the selected solid with its dimension labels as you type.
Frequently Asked Questions
What is total surface area?
Total surface area is the sum of every face of a 3D shape — the base(s) plus the lateral (side) surface. It is the amount of area you would cover if you wrapped the whole solid.
How do you find the surface area of a cylinder?
A cylinder uses S = 2πr(r + h): the 2πr² part is its two circular bases and the 2πrh part is the curved side. Enter the radius r and height h and the tool combines them for you.
What is the surface area formula for a cube?
A cube has six equal square faces, so its surface area is S = 6 × a², where a is the side length. For a = 5, that is 6 × 25 = 150 square units.
How is a cone's surface area calculated?
A cone uses S = πr(r + √(r² + h²)). The √(r² + h²) term is the slant height, so the formula adds the circular base (πr²) to the curved lateral surface.
What is the difference between lateral and total surface area?
Lateral surface area counts only the side faces, leaving out the base(s). Total surface area adds the base(s) back in. This calculator reports the total surface area for each solid.
What units is surface area measured in?
Surface area is always in square units. Enter dimensions in cm and the result is cm²; use m and it becomes m², and likewise for mm², in², and ft².
What is the difference between surface area and volume?
Surface area measures the outer skin of a solid in square units, while volume measures the space inside in cubic units. Use the volume tab of the calculator for the space a shape holds.
No comments yet. Be the first to comment!