Quick answer
Surface area formulas: sphere 4πa², cube 6a², cylinder 2πa(a + b), cone πa(a + √(a² + b²)) and box 2(ab + ac + bc). A sphere of radius 1 has a surface area of 12.5664.
Choose a shape and enter its dimensions. The calculator returns the surface area.
Related tools: Surface Area of a Cylinder Calculator: Surface area and volume of a cylinder. Cuboid Surface Area Calculator: Surface area of a cuboid. Hemisphere Surface Area Calculator: Curved and total surface area of a hemisphere.
How to use the Surface Area Calculator
- Choose shape: Sphere (a = radius), Cube (a = side), Cylinder (a = radius, b = height), Cone (a = radius, b = height) and Box (a, b, c = sides).
- Enter a (above 0).
- Optionally, enter b (above 0).
- Optionally, enter c (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Shape | Choose one: Sphere (a = radius); Cube (a = side); Cylinder (a = radius, b = height); Cone (a = radius, b = height); Box (a, b, c = sides) | Starts at Sphere (a = radius) |
| a | A number | > 0 |
| b (optional) | A number | > 0 |
| c (optional) | A number | > 0 |
Formula and method
Formula
sphere 4πa²; cube 6a²; cylinder 2πa(a+b); cone πa(a+√(a²+b²)); box 2(ab+ac+bc)
IEEE-754 double precision; shown to at most 6 decimal places.
Standard surface-area formulas; unused dimensions are ignored.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Shape = Sphere (a = radius); a = 1.
| Result | Value |
|---|---|
| Surface area | 12.566371 |
Example 2
Inputs: Shape = Cube (a = side); a = 2.
| Result | Value |
|---|---|
| Surface area | 24 |
Example 3
Inputs: Shape = Cylinder (a = radius, b = height); a = 3; b = 5.
| Result | Value |
|---|---|
| Surface area | 150.796447 |
The first line is the headline result (surface area). IEEE-754 double precision; shown to at most 6 decimal places.
Shapes covered
Sphere (a = radius), cube (a = side), cylinder (a = radius, b = height), cone (a = radius, b = height) and box (a, b, c). Shapes that need b or c require them.
Uses
Surface area tells you how much paint, wrapping or material covers a solid. A cube of side 3 has 54 square units; a cylinder r = 3, h = 5 has 150.8. Use consistent units.
How the result changes with a
Holding every other input at the first worked example, this table changes only a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| a | Surface area |
|---|---|
| 0.5 | 3.141593 |
| 1 | 12.566371 |
| 2 | 50.265482 |
| 4 | 201.06193 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- b: left empty shows "Enter b for this shape." beside that field and no result.
- c: left empty shows "Enter c for a box." beside that field and no result.
Choosing between the Surface Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Surface Area of a Cylinder Calculator](/math/surface-area-of-cylinder/) | radius and height | Surface area |
| [Cuboid Surface Area Calculator](/math/cuboid-surface-area/) | length, width and height | Surface area |
| [Hemisphere Surface Area Calculator](/math/area-of-hemisphere/) | radius | Curved surface area |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Shapes needing b or c require them
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for b and c to confirm this.
Frequently asked questions
What is the surface area of a cube with side 4?
A cube with side 4 has surface area 6 × 16 = 96.
Does a cylinder's area include the ends?
Yes. The cylinder formula 2πa(a + b) includes both circular ends and the curved side.
Which shape has the least area for a given volume?
The sphere has the least surface area for a given volume.
What does the Surface Area Calculator calculate?
Surface area of a sphere, cube, cylinder, cone or box. It returns Surface area.
What formula does the Surface Area Calculator use?
sphere 4πa²; cube 6a²; cylinder 2πa(a+b); cone πa(a+√(a²+b²)); box 2(ab+ac+bc). Standard surface-area formulas; unused dimensions are ignored.
What do I need to enter in the surface Area Calculator?
You enter Shape and a. Optional: b and c.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Shapes needing b or c require them.
What does the “Shape” option change?
It sets how the surface Area is worked out. The choices are Sphere (a = radius), Cube (a = side), Cylinder (a = radius, b = height), Cone (a = radius, b = height) and Box (a, b, c = sides).
What is an example of a surface Area result?
With shape Sphere (a = radius) and a 1, the surface area is 12.566371.
Related calculators
- Surface Area of a Cylinder Calculator — Surface area and volume of a cylinder.
- Cuboid Surface Area Calculator — Surface area of a cuboid.
- Hemisphere Surface Area Calculator — Curved and total surface area of a hemisphere.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.