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Surface Area Calculator

Calculate the surface area of 8 geometric shapes including sphere, cylinder, cone, cuboid, rectangular prism, triangular prism, square pyramid, and tetrahedron with detailed step-by-step solutions and interactive diagrams.

Surface Area Calculator
Sphere Cylinder Cone Cuboid Rect Prism Tri Prism Pyramid Tetrahedron

Sphere Surface Area

Calculate the surface area of a sphere given its radius

Formula
\( A = 4\pi r^2 \)
Quick Examples:
r = 5 r = 3.5 r = 10 r = 7.25

Cylinder Surface Area

Calculate total surface area including both circular bases

Formula
\( A = 2\pi r(r + h) \)
Quick Examples:
r=3, h=7 r=5, h=10 r=2.5, h=8

Cone Surface Area

Calculate surface area including base and lateral surface

Formula
\( A = \pi r(r + l) \) where \( l = \sqrt{r^2 + h^2} \)
Quick Examples:
r=4, h=6 r=3, h=5 r=5, h=12

Cuboid Surface Area

Calculate the total surface area of a rectangular box

Formula
\( A = 2(lw + lh + wh) \)
Quick Examples:
5 x 4 x 3 6 x 6 x 6 8 x 5 x 2

Rectangular Prism Surface Area

Calculate total surface area of a 3D rectangular shape

Formula
\( A = 2(lw + lh + wh) \)
Quick Examples:
6 x 4 x 3 10 x 5 x 2 7 x 7 x 4

Triangular Prism Surface Area

Calculate area of two triangular bases and three rectangular sides

Formula
\( A = bh + (a + b + c) \times l \) (where a, b, c are triangle sides)
Quick Examples:
b=4, h=5, l=6 b=3, h=4, l=8 b=6, h=5, l=10

Square Pyramid Surface Area

Calculate base area plus four triangular face areas

Formula
\( A = a^2 + 2al \) where \( l = \sqrt{(a/2)^2 + h^2} \)
Quick Examples:
a=5, h=7 a=4, h=6 a=8, h=10

Tetrahedron Surface Area

Calculate surface area of a regular tetrahedron (4 equilateral triangles)

Formula
\( A = \sqrt{3} \cdot a^2 \)
Quick Examples:
a = 3 a = 5 a = 8 a = 10

Embed Surface Area Calculator Widget

About Surface Area Calculator

Welcome to our comprehensive Surface Area Calculator, a powerful tool designed to compute the surface area of various three-dimensional geometric shapes with detailed step-by-step solutions. Whether you are a student learning geometry, an educator preparing lessons, or a professional working on engineering or architectural projects, this calculator provides accurate results with clear explanations.

What is Surface Area?

Surface area is the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces (or surfaces) that enclose the object. Surface area is measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).

Understanding surface area is crucial in many real-world applications including:

Supported Shapes and Formulas

Sphere

Formula: \( A = 4\pi r^2 \)
A perfectly symmetrical 3D shape where every point on the surface is equidistant from the center.

Cylinder

Formula: \( A = 2\pi r(r + h) \)
Has two parallel circular bases connected by a curved surface.

Cone

Formula: \( A = \pi r(r + l) \) where \( l = \sqrt{r^2 + h^2} \)
Has a circular base tapering to a single point (apex).

Cuboid / Rectangular Prism

Formula: \( A = 2(lw + lh + wh) \)
A 3D shape with six rectangular faces.

Triangular Prism

Formula: \( A = bh + (a + b + c)l \)
Has two triangular bases and three rectangular sides.

Square Pyramid

Formula: \( A = a^2 + 2al \) where \( l = \sqrt{(a/2)^2 + h^2} \)
Has a square base and four triangular faces meeting at an apex.

Tetrahedron

Formula: \( A = \sqrt{3}a^2 \)
A regular polyhedron with four equilateral triangular faces.

How to Use This Calculator

  1. Select a Shape: Click on one of the eight shape icons in the selector to choose the geometric shape you want to calculate.
  2. Enter Dimensions: Input the required measurements (such as radius, height, length, width, or edge length) in the provided fields.
  3. Calculate: Click the "Compute Surface Area" button to get your result.
  4. Review the Solution: Examine the step-by-step solution to understand how the surface area was calculated.

Understanding the Results

Our calculator provides:

Frequently Asked Questions

What is Surface Area?

Surface area is the total area that the surface of a three-dimensional object occupies. It is measured in square units (like square meters, square feet, etc.) and represents the sum of the areas of all faces or surfaces of a 3D shape.

How do you calculate the surface area of a sphere?

The surface area of a sphere is calculated using the formula \( A = 4\pi r^2 \), where \( r \) is the radius of the sphere. For example, a sphere with radius 5 has a surface area of \( 4 \times \pi \times 25 \approx 314.16 \) square units.

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

Lateral surface area refers to the area of all sides of a 3D shape excluding the base(s). Total surface area includes all surfaces, including the base(s). For example, a cylinder's lateral surface area is \( 2\pi rh \) (the curved surface), while the total surface area is \( 2\pi r(r + h) \) which includes both circular bases.

What shapes can this calculator compute?

This calculator computes surface area for 8 geometric shapes: Sphere, Cylinder, Cone, Cuboid, Rectangular Prism, Triangular Prism, Square Pyramid, and Tetrahedron. Each shape has its own formula and the calculator provides step-by-step solutions.

Additional Resources

Reference this content, page, or tool as:

"Surface Area Calculator" at https://MiniWebtool.com/surface-area-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 16, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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