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Cylinder Calculator

Name: Cylinder Calculator
Availability: InStock
Author: Calculat

Calculate right circular cylinder volume, total surface area, lateral (curved) surface area, and base area from radius and height.

Radius (r)

Height (h)

Cylinder Geometry

Volume

226.1947

Total Surface Area

207.3451

Curved (Lateral) Area

150.7964

Base Area (Single)

28.2743

Deduction Steps:

Radius r = 3, Height h = 8

Diameter: d = 2r = 6

Base Area (Single): A_base = πr² = π × (3)² = 28.2743

Lateral (Curved) Surface Area: A_lat = 2πrh = 2 × π × 3 × 8 = 150.7964

Total Surface Area: A_total = 2A_base + A_lat = 2(28.2743) + 150.7964 = 207.3451

Volume: V = πr²h = 28.2743 × 8 = 226.1947

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What Is a Cylinder Calculator?

A right circular cylinder is a three-dimensional solid formed by two congruent circular bases in parallel planes connected by a curved surface perpendicular to both bases.

How to Use This Calculator

Enter the radius (r) and height (h) of the cylinder.
View the calculated Volume, Total Surface Area, Lateral Surface Area, and Base Area.
Review the step-by-step mathematical breakdown using π ≈ 3.14159265.

Cylinder Volume and Surface Area Formulas

V = \pi r^2 h, \quad A_{\text{lat}} = 2\pi r h, \quad A_{\text{total}} = 2\pi r(r + h)

Volume equals base circular area (πr²) multiplied by height. Lateral area unrolls into a rectangle of width 2πr and height h.

Worked Example

Scenario: Find volume and surface area of a cylinder with radius r = 3 cm and height h = 10 cm

Base Area: A_base = π × 3² = 9π ≈ 28.2743 cm²

Volume: V = 9π × 10 = 90π ≈ 282.7433 cm³

Lateral Area: A_lat = 2 × π × 3 × 10 = 60π ≈ 188.4956 cm²

Total Surface Area: A_total = 2(28.2743) + 188.4956 ≈ 245.0442 cm²

Result: Volume ≈ 282.74 cm³, Total Surface Area ≈ 245.04 cm²

Tips & Key Notes

If you know diameter, divide by 2 to get radius before calculating.
The unrolled lateral surface of a cylinder is a flat rectangle with dimensions 2πr by h.
To find capacity in liters from cubic centimeters (cm³), divide volume by 1,000.

Frequently Asked Questions

What is the curved surface area of a cylinder?

The curved (lateral) surface area is 2πrh, representing only the outer cylinder wall without the circular top and bottom caps.

How do you find cylinder volume from diameter?

Radius is diameter / 2. Then V = π × (d/2)² × h = (π/4) × d² × h.

What is an oblique cylinder?

An oblique cylinder is one where the centers of the circular bases are not aligned perpendicularly. By Cavalieri’s principle, its volume is still V = πr²h.