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Cylinder Calculator

A cylinder is a three-dimensional solid with two congruent, parallel circular bases joined by a curved cylindrical lateral surface. This free Cylinder

Mathematics
Formula & Methodology
Volume = π × Radius² × Height = πr²h Lateral Surface Area = 2 × π × Radius × Height = 2πrh Total Surface Area = 2πrh + 2πr²

To solve a cylinder given radius (r) and height (h): 1. Compute base circular area: πr². 2. Multiply base area by height to obtain internal volume: V = πr²h. 3. Compute the unrolled rectangular lateral wall area: 2πrh. 4. Add the areas of the top and bottom circular bases (2 × πr²) to the lateral wall to yield the total surface area.

Cylinder Volume (πr²h)

502.6548

Overview

A cylinder is a three-dimensional solid with two congruent, parallel circular bases joined by a curved cylindrical lateral surface. This free Cylinder Calculator computes the interior volume, total surface area, lateral wall area, and circular base area concurrently.

Cylinder calculations are vital for sizing industrial storage silos, chemical pipeline capacities, hydraulic fluid pistons, automotive engine displacement (bore and stroke), and beverage cans.

Worked Examples

Example 1: Cylinder with Radius = 4, Height = 10

Inputs: Radius = 4, Height = 10

  1. Volume: π × 4² × 10 = π × 16 × 10 = 160π ≈ 502.65.
  2. Lateral area: 2π × 4 × 10 = 80π ≈ 251.33.
  3. Base areas: 2 × π × 16 = 32π ≈ 100.53.
  4. Total Surface Area: 80π + 32π = 112π ≈ 351.86.
Final Answer: Volume: 502.65, Total SA: 351.86

Example 2: Coffee Can (Radius 3 in, Height 6 in)

Inputs: Radius = 3, Height = 6

  1. Volume: π × 9 × 6 = 54π ≈ 169.65 cu in.
  2. Total SA: 2π(3)(6) + 2π(9) = 36π + 18π = 54π ≈ 169.65 sq in.
Final Answer: Volume: 169.65, Surface Area: 169.65

Example 3: Hydraulic Piston (Radius 2 cm, Stroke 15 cm)

Inputs: Radius = 2, Height = 15

  1. Volume = π × 4 × 15 = 60π ≈ 188.50 cm³.
Final Answer: 188.50 cm³ Displacement

How to Use This Calculator

  1. Enter the cylinder radius into the first input field.
  2. Enter the cylinder height into the second input field.
  3. Click "Calculate" to view the volume and surface areas.
  4. Review the lateral wall area and individual base areas below.
  5. Click "Reset" to analyze another cylinder.

Reference Table

Radius (r)Height (h)Volume (πr²h)Total Surface Area
2562.8387.96
310282.74245.04
410502.65351.86
512942.48534.07
6151696.46791.68

Frequently Asked Questions

What is the lateral area of a cylinder?
The lateral area is the surface area of the curved tube wall only, excluding the circular top and bottom lids.
How does an engine's bore and stroke relate to a cylinder?
The "bore" is the cylinder's diameter (so radius = bore / 2), and the "stroke" is the cylinder height. Engine displacement equals π × (bore/2)² × stroke × number of cylinders.
What shape does the curved lateral wall form when unrolled flat?
When unrolled flat, the curved wall forms a perfect rectangle with width equal to the base circumference (2πr) and length equal to the height (h).
How do you convert cylinder cubic inches to fluid ounces?
One fluid ounce equals approximately 1.80469 cubic inches. Divide cubic inches by 1.805 to find liquid ounces.
Can a cylinder have an elliptical base?
Yes, that is an elliptic cylinder. This calculator focuses on the standard right circular cylinder.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via rotational solid cylindrical coordinates integration.