What is the difference between surface area and volume?

Surface area is the total area of all outer faces of a 3D object (measured in square units). Volume is the amount of space the object occupies (measured in cubic units).

What is the slant height of a cone?

The slant height l is the distance from the apex to the edge of the base along the side: l = √(r² + h²). It differs from the vertical height h.

Can I use this for real-world applications?

Yes. Surface area calculations are used for painting, wrapping, coating, and material estimation. Volume calculations help with capacity, weight, and fluid problems.

What units should I use?

Use consistent units for all dimensions. The surface area will be in the square of your input unit, and volume in the cube.

How is a rectangular prism different from a cube?

A cube has all equal sides (a × a × a). A rectangular prism (cuboid) can have three different side lengths (l × w × h).

Math

↵ to calculate

Surface Area Calculator — Sphere Cylinder Cone Box

Calculate the surface area and volume of spheres, cylinders, cones, cubes, and rectangular prisms.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

📏 Some countries say ‘30 degrees’ and others say ‘86 degrees’ for the same weather! Some say ‘5 km’, others say ‘3 miles’. This tool swaps between them instantly so you always know what it means.

📌 Direct Answer & Summary

The surface area calculator computes the total surface area and volume for five common 3D shapes: sphere, cylinder, cone, cube, and rectangular prism. Select a shape, enter the required dimensions, and get both measurements instantly.

Shape

What is Surface Area Calculator — Sphere Cylinder Cone Box?

How to use it

1️⃣ Select the 3D shape from the dropdown menu.
2️⃣ Enter the required dimensions (radius, height, side lengths).
3️⃣ Click Calculate to see surface area and volume.
4️⃣ Switch shapes to calculate different geometries.
5️⃣ All inputs accept decimal values.

Formula

Sphere: SA = 4πr², V = (4/3)πr³. Cylinder: SA = 2πr² + 2πrh, V = πr²h. Cone: SA = πr² + πrl (l=√(r²+h²)), V = (1/3)πr²h. Cube: SA = 6a², V = a³. Rect. prism: SA = 2(lw+lh+wh), V = lwh.

💡 See it in action — a real example

Cylinder with r=3, h=10: SA = 2π(9) + 2π(3)(10) = 18π + 60π = 78π ≈ 245.04. V = π(9)(10) = 90π ≈ 282.74.

❓ Common questions

What is the difference between surface area and volume?: Surface area is the total area of all outer faces of a 3D object (measured in square units). Volume is the amount of space the object occupies (measured in cubic units).
What is the slant height of a cone?: The slant height l is the distance from the apex to the edge of the base along the side: l = √(r² + h²). It differs from the vertical height h.
Can I use this for real-world applications?: Yes. Surface area calculations are used for painting, wrapping, coating, and material estimation. Volume calculations help with capacity, weight, and fluid problems.
What units should I use?: Use consistent units for all dimensions. The surface area will be in the square of your input unit, and volume in the cube.
How is a rectangular prism different from a cube?: A cube has all equal sides (a × a × a). A rectangular prism (cuboid) can have three different side lengths (l × w × h).

⚡ Related Math Tools & Calculators

Circle Calculator Pythagorean Theorem Volume Calculator