Radius of a Cylinder Calculator

Calculate the radius of a cylinder using various geometric parameters and formulas

Calculate Cylinder Radius

The height of the cylinder

The volume of the cylinder

Calculation Results

0.000000
Radius (r)

Formula used: r = √(V / (π × h))

Calculation Analysis

Example Calculation

Water Tank Example

Problem: A cylindrical water tank has a volume of 500 liters and height of 2 meters

Given: Volume = 0.5 m³, Height = 2 m

Find: Radius of the tank

Solution

Using formula: r = √(V / (π × h))

r = √(0.5 / (π × 2))

r = √(0.5 / 6.283)

r = √(0.0796)

r = 0.282 meters

Cylinder Formulas

Volume

V = π × r² × h

Base Area

A_b = 2 × π × r²

Lateral Area

A_l = 2 × π × r × h

Total Surface Area

A = A_b + A_l

Diagonal

d = √(4r² + h²)

Calculator Tips

Choose the method based on known parameters

Ensure all input values use consistent units

Radius is half the diameter of the base

Base area includes both top and bottom circles

Diagonal is the longest distance in the cylinder

Understanding Cylinder Radius Calculations

What is a Cylinder Radius?

The radius of a cylinder is the distance from the center of the circular base to any point on the circumference. It's a fundamental measurement that determines all other properties of the cylinder including volume, surface area, and capacity.

Key Properties

  • Radius determines the circular cross-section
  • Diameter equals twice the radius
  • Volume increases with the square of radius
  • Surface area depends on both radius and height

Common Applications

  • Engineering design and manufacturing
  • Tank and pipe capacity calculations
  • Architecture and construction
  • Material science and physics

Pro Tip: When working with real-world problems, always verify that your calculated radius makes physical sense given the context and constraints.

Formula Derivations

From Volume and Height

V = π × r² × h

r² = V / (π × h)

r = √(V / (π × h))

From Lateral Area and Height

A_l = 2 × π × r × h

r = A_l / (2 × π × h)