yCalculator

Surface Area Calculator

Last updated: June 2026

Choose a 3D shape

Calculate the outside covering area of common solids.

Dimensions

surface area = outside covering3D shape plus labelled surface components

Total surface area

188.4956 cm²

SA = 2pi r^2 + 2pi rh

Component breakdown

Base area

56.5487 cm²

Lateral area

131.9469 cm²

Total

188.4956 cm²

Step-by-step working

Formula: SA = 2pi r^2 + 2pi rh

Substitution: SA = 2pi x 3 x 7 + 2pi x 3^2

  1. Area of two circular ends = 2 x pi x 3^2 = 56.5487 cm^2
  2. Lateral area = 2 x pi x 3 x 7 = 131.9469 cm^2
  3. Total = 188.4956 cm^2

Also calculate volume?

Volume Calculator

Surface area vs volume

Surface area measures the outside covering of a 3D shape in square units. Volume measures the space inside in cubic units.

Net diagrams and surface area

A net unfolds a 3D shape into flat faces. Adding the area of each face gives total surface area.

Real-world surface area applications

Surface area is used for painting, wrapping, packaging, insulation, coating, fabric, and material estimates.

About this calculator

The Surface Area Calculator finds the outside area of common 3D shapes such as cubes, rectangular prisms, cylinders, cones, spheres, pyramids, triangular prisms, capsules, and toruses. It is useful for packaging, painting, wrapping, material estimates, and geometry revision.

surface area calculator method

Surface area adds the areas of all outside faces or curved surfaces. The exact formula depends on the selected 3D shape.

  • Cube: SA = 6s^2
  • Rectangular prism: SA = 2(lw + lh + wh)
  • Sphere: SA = 4pi r^2
  • Cylinder: SA = 2pi r^2 + 2pi rh
  • Cone: SA = pi r^2 + pi r l
  • Triangular prism: SA = bh + (s1+s2+s3) x length

How to use the surface area calculator

  1. Choose the 3D shape.
  2. Enter the relevant dimensions.
  3. Choose whether bases or end caps should be included where the calculator offers that option.
  4. Calculate each face or curved surface area.
  5. Add the surface components together.
  6. Read the total surface area in square units.

Worked examples

Cube

Input: s = 4

Calculation: SA = 6 x 4^2

Result: 96 square units

Cylinder

Input: r = 3, h = 7

Calculation: SA = 2pi r^2 + 2pi rh

Result: About 188.5 square units

Surface area vs volume

Surface area measures the outside covering of a 3D object. Volume measures the space inside it. A box can have the same volume as another box but a different surface area.

Practical geometry checks

Use one unit system
Keep all lengths in the same unit before calculating. Mixing centimetres, metres, inches, or feet in the same formula will produce misleading results.
Perimeter vs area
Perimeter is a distance around the outside. Area is the amount of flat space inside a shape. Surface area is the total outside covering of a 3D shape.
Rounded answers
Pi, square roots, and trigonometric values are often irrational, so decimal answers are approximations. Keep extra decimal places until the final result.

Edge cases

  • Zero or negative dimensions do not describe a real physical shape.
  • Regular polygon formulas assume all sides and angles are equal.
  • Circle and ellipse formulas use pi, so most decimal answers are rounded.
  • A trapezoid/trapezium perimeter needs all four side lengths, not just the parallel sides and height.

Limitations

This calculator is for educational and planning use. For construction, manufacturing, surveying, engineering, or safety-critical work, confirm dimensions, tolerances, and rounding rules with the appropriate professional method or specification.

Frequently asked questions

What units should I enter?

Use any length unit you like, but keep every length in the same unit. If you enter metres, area is in square metres and surface area is also in square metres.

Why are some answers approximate?

Calculations involving pi, square roots, or curved shapes often produce irrational numbers. The calculator rounds the displayed decimal result.

What is the difference between area and surface area?

Area measures a flat 2D region. Surface area measures the total outside area of a 3D object.

Can I use these calculators for homework?

Yes. They are useful for checking answers and understanding formulas, but you should still show the working required by your class or exam.

Do regular polygon formulas work for irregular polygons?

No. Regular polygon formulas assume equal sides and equal angles. Irregular polygons usually need to be split into simpler shapes.

Related calculators

  • Volume Calculator
  • Area Calculator
  • Rectangle Calculator

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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