Surface Area Calculator

What this calculator does

The Surface Area Calculator measures the total area of the outer surface of a cube, rectangular box, cylinder, cone, or sphere. Surface area is expressed in square units, such as square feet, square meters, or square inches. Enter every dimension in the same unit, and the result is reported in that unit squared.

Surface area is useful when estimating paint, coating, wrapping, insulation, and heat-transfer area. A cube or box surface area describes how much material covers all six faces. A cylinder or cone surface area includes curved and flat surfaces. A sphere surface area describes the outside of a ball-shaped object.

How to use this calculator

1. Choose the solid: cube, rectangular box, cylinder, cone, or sphere.
2. Enter the dimensions requested for that solid.
3. Click Calculate.
4. Read the total surface area and the supporting values.

The default cube has an edge of 5 and a surface area of 150 square units. The box example is 10 by 5 by 4 and gives 220. A cylinder with radius 3 and height 4 has a surface area of about 131.9469. A cone with the same radius and height has a surface area of about 75.3982, and a sphere with radius 3 has a surface area of about 113.0973.

Surface area formulas

Cube:     SA = 6a²
Box:      SA = 2(lw + lh + wh)
Cylinder: SA = 2πr² + 2πrh
Cone:     SA = πr² + πrl, where l = √(r² + h²)
Sphere:   SA = 4πr²

In these formulas, a is the cube edge, l, w, and h are the box dimensions, r is the base radius, h is the perpendicular height, and l is the cone's slant height.

What the results mean

The highlighted result is the total surface area. The supporting rows separate the lateral surface from the base area when that distinction is useful, and they also show the solid's volume. For a cone, the slant height is reported because the curved surface depends on it.

For a cylinder, the total surface includes both circular ends and the curved side. The lateral surface includes only the curved side. For a cone, the total surface includes the circular base and the curved side.

Assumptions and limitations

• All dimensions must use the same unit. No unit conversion is performed.
• Every dimension must be greater than zero.
• The box is a right rectangular prism, the cylinder is a right circular cylinder, and the cone is a right circular cone.
• The sphere is a perfect sphere.
• The calculator does not account for thickness, openings, overlaps, seams, or waste when estimating materials.
• Results involving π are approximations and are rounded for display.

Frequently asked questions

What is the difference between lateral area and total surface area?

Lateral area covers only the curved or side portion of a solid. Total surface area also includes the flat base or bases. For a closed container, total surface area is usually the right value for material estimates. For an open container, subtract the missing base.

Why does the cone formula use slant height?

The curved surface of a cone unrolls into a sector of a circle whose radius is the slant height. The slant height is the distance from the tip to the edge of the base, not the perpendicular height. It is calculated from the radius and height with the Pythagorean theorem.

Can I use this calculator for a pyramid?

Not directly. A square pyramid is a different solid with triangular side faces, and its surface area depends on the base edge and slant height. This page covers cubes, rectangular boxes, cylinders, cones, and spheres only.

Reference table

Surface area unit conversions

Source

Reference: Calculator.net — Surface Area Calculator.

This page is for general educational and estimation purposes. Add an allowance for seams and waste before purchasing coating or wrapping materials.