Surface Area Calculator: Calculate Surface

This free online Surface Area Calculator can find the surface area of a 3D object. The surface area is the total area of an object’s exterior. This includes the areas of all faces, curves and bases.

The surface area calculation is often used in mathematics as well as in construction, engineering, architecture, manufacturing and everyday life. This could be used to calculate how much paint is needed to paint a wall or how much material is needed to manufacture a box.

There are many formulas you can use to calculate the surface area of different 3D objects. For example, a cube has 6 identical square faces, a cylinder has 2 circular bases and 1 curved surface and a sphere has a fully curved exterior.

Our Surface Area Calculator will help you calculate the surface area of a 3D object quickly. Just enter the measurements needed.

Depending on what options are available you can calculate the surface area of common geometric objects like:

• Cube
• Rectangular Prism (Cuboid)
• Sphere
• Cylinder
• Cone
• Triangular Prism
• Pyramid

This surface area calculator can help you quickly calculate surface area problems whether you’re a student, teacher, contractor, engineer or DIY lover!

How to Use the Surface Area Calculator

Using our online Surface Area Calculator is very simple. Follow the steps below to calculate the surface area of your 3D object.

Select your 3D Shape – Choose the shape you want to calculate the surface area of e.g cube, sphere, cylinder, cone, rectangular prism.

Enter the Measurements – Enter the measurements needed e.g length, width, height, radius, slant height.

Choose your Measurement – Choose your measurement e.g inches, feet, centimetres, metres.

Check Measurements – Ensure the measurements are all positive.

Click Calculate – Click calculate.

View your Results – The surface area of your 3D object will be shown in the relevant square units.

Example

Let’s say we want to calculate the surface area of a cube with a side length of 5 inches.

Cube

Side Length = 5 inches

Formula = 6 x Side²

Surface Area =

6 × 5² = 150 Square Inches.

Result = 150 in²

You can calculate the surface area of different geometric objects using this calculator.

Surface Area Calculator Formula

There are different formulas you can use to calculate the surface area of a 3D object. Below are the formulas for common geometric objects.

Cube

This object contains 6 identical square faces.

SA = 6a²

Where:

SA = Surface Area

a = Length of 1 side

Rectangular Prism

This object contains 6 rectangular faces.

SA=2(lw + lh + wh)

Where:

l = Length

w = Width

h = Height

Sphere

This object contains 1 complete curved surface.

SA=4πr²

Where:

r = Radius

π ≈ 3.14159

Cylinder

This object has 2 circular bases and 1 curved surface.
SA=2πr² + 2πrh

Where:

r = Radius

h = Height

Cone

The total surface area of a right circular cone is:

SA = πr² + πrl

Where:

r = Radius of base

l = Slant height

Triangular Prism

The total surface area of a triangular prism is:

SA = 2B + Ph

Where:

B = Area of triangular base

P = Perimeter of triangular base

h = Length of prism

Square Pyramid

The total surface area of a regular square pyramid is:

SA=a^2 + 2al

Where:

a = Length of base side

l = Slant height

Example Calculation

Let’s take a look at some examples of how to calculate surface area.

Example 1: Surface Area of a Cube

Let’s say we have a cube with a side length of 4 inches.

a = 4 inches

SA = 6a²

SA = SA=6 x 4²

SA = SA=6 x 16

SA = SA=96 in²

Result = 96 Square Inches.

Example 2: Surface Area of a Rectangular Prism

Let’s say we have a rectangular box with the following measurements:

Length = 10 inches

Width = 5 inches

Height = 4 inches

Formula = SA=2(lw + lh + wh)

SA = SA=20__((10 x 5) + (10 x 4) + (5 x 4))

SA = SA=21__(50 + 40 + 20)

SA = SA=22__ x 110

SA = SA=23__ in²

Result = 220 Square Inches.

Example 3: Surface Area of a Sphere

Let’s say we have a sphere with a radius of 3 feet.

r = 3 feet

SA = 4πr²

SA = SA=24__ x 3.14159 x 3²

SA = SA=25__ x 3.14159 x 9

SA ≈ 113.10 ft²

Result = 113.10 Square Feet.

Now we understand how to calculate the surface area of different geometric objects using different formulas.

Understanding Your Results

When using a Surface Area Calculator your result will tell you the total area of an object’s exterior.

Depending on your chosen shape your result may be shown in square inches (in²), square feet (ft²), square centimetres (cm²) or square metres (m²).

Some key terms to know:

Total Surface Area – The total area of all the exterior surfaces.

Lateral Surface Area – The area of the sides only, not including the base(s).

Base Area – The area of the base/top of an object.

Curved Surface Area – The area of a curved surface.

Square Units – Surface area is always shown in square units as it is a 2D measurement.

For example, if the surface area of a rectangular box was 220 square inches this would mean that the total area of the 6 exterior faces is 220 square inches.

Understanding these terms will help you choose the correct measurement for your calculation.

Factors that Affect Surface Area

There are a few factors that affect the surface area of 3D objects.

Shape – Different geometric shapes have different formulas for calculating their surface area. A sphere, cube and cylinder cannot be calculated using the same formula.

Length, Width & Height – If you’re calculating the surface area of a rectangular prism changing any of these measurements will affect the total surface area.

Radius – The radius has a large effect on the surface area of spheres, cylinders and cones. The larger the radius the larger the surface area.

Slant Height – The slant height is an important measurement when calculating the surface area of cones and pyramids.

Number of Faces – If an object has more faces or more exposed faces then the total surface area may be larger.

Units – The units you use will affect how your final answer is shown. Ensure all measurements are in the same units.

Open/Closed – An open object may have a different surface area than a closed object as 1 or more faces may not be included.

Advantages and Uses of a Surface Area Calculator

There are many benefits to using a Surface Area Calculator.

• Saves Time – You can calculate the surface area of different 3D objects in seconds.
• Helps Students – Students can use this to practice their geometry problems, check their homework answers and understand mathematical formulas.
• Helps with Construction – Contractors can use this to calculate how much material they may need to cover walls, floors, roofs etc.
• Helps with Painting – Calculate how much area you need to paint before buying paint, coatings or protection.
• Helps with Packaging – Manufacturers can calculate how much material they may need to make boxes, containers and packaging.
• Helps with Engineering – Engineers can use the surface area to design equipment, parts and products.
• Minimises Errors – The calculations are done automatically which reduces errors that can happen with complicated formulas.
• Helps with DIY – Home owners can calculate how much material they need to paint furniture, cover objects and complete DIY projects.

Accuracy, Assumptions & Limitations

If you enter the correct shape and measurements into the calculator you will get an accurate result.

However there are some things to note.

• Accurate Measurements – To ensure accurate results you need to enter accurate measurements. This includes length, width, height, radius and anything else needed.
• Regular Shapes – Most formulas assume the object is a perfect regular geometric shape. In real life objects may have uneven surfaces.
• Same Units – All measurements need to be in compatible units. If you use inches and feet without converting this may give you inaccurate results.
• Closed/Open – Some formulas will calculate the total surface area of a closed object. If you’re calculating for an open object you may need to exclude 1 or more faces.
• Rounded – Answers with π in them may be rounded to a number of decimal places.
• No Consideration for Material – The surface area doesn’t automatically take into consideration how thick the paint/material is, wastage, overlap or cutting.
• Irregular Objects – If you have an irregular object or a combination of 3D objects you may need to split them into smaller geometric pieces and calculate each surface individually.

In practical situations you may want to allow extra for wastage, overlap and installation. Always double check your measurements before purchasing materials for construction/ manufacturing.

FAQs

What is a Surface Area Calculator?

A Surface Area Calculator is an online tool that can calculate the total exterior area of a 3D object. This can be used to calculate the surface area of objects such as cubes, spheres, cylinders, cones and rectangular prisms.

What is the formula for surface area?

This depends on the shape, for a cube it is SA = 6a², for a rectangular prism it is SA=26__(lw + lh + wh) and for a sphere it is SA = 4πr².

What is the difference between surface area and volume?

The surface area of an object is the total area of the exterior whereas the volume is the amount of 3D space inside. Surface area is measured in square units whereas volume is measured in cubic units.

Can I calculate surface area in square feet and square inches?

Yes! You can calculate the surface area using different measurements. This can include square feet, square inches, square metres and square centimetres. Ensure all your measurements are in compatible units.

How can a Surface Area Calculator help with construction?

Contractors and builders can use the surface area to calculate how much paint, roofing, wall coverings, insulation etc they may need for their project.