Circumference to Volume Calculator

| Added in Math & Numbers

What is a Circumference to Volume Calculator?

A circumference to volume calculator helps you calculate the volume of a cylinder when you know its circumference and length. This is particularly useful when measuring cylindrical objects where the circumference is easier to measure than the diameter or radius.

Formula

The formula for calculating volume from circumference is:

$$
\text{Volume} = \pi \times \left(\frac{C}{2\pi}\right)^2 \times L
$$

Where:

  • C = Circumference of the circular cross-section
  • L = Length (or height) of the cylinder
  • Ο€ (pi) β‰ˆ 3.14159

This formula works by first converting the circumference to radius using r = C / (2Ο€), then applying the standard cylinder volume formula V = Ο€rΒ²h.

How to Use This Calculator

  1. Enter the Total Circumference: Input the circumference measurement of your cylinder
  2. Select the Unit: Choose either inches (in) or centimeters (cm)
  3. Enter the Length: Input the length or height of the cylinder
  4. Click Calculate: The calculator will display the volume in cubic inches (inΒ³) or cubic centimeters (cmΒ³)

Example Calculation

Let's calculate the volume of a cylinder with:

  • Circumference: 40 inches
  • Length: 10 inches

Step-by-step calculation:

  1. Find the radius: r = 40 / (2Ο€) = 40 / 6.2832 β‰ˆ 6.366 inches
  2. Square the radius: rΒ² = 6.366Β² β‰ˆ 40.543
  3. Calculate volume: V = Ο€ Γ— 40.543 Γ— 10 β‰ˆ 1273.24 inΒ³

Result: The volume is approximately 1273.24 cubic inches.

Common Applications

  • Pipe and Tubing: Calculate internal volume for plumbing or HVAC systems
  • Cylindrical Tanks: Determine storage capacity when only circumference is known
  • Manufacturing: Quality control when measuring cylindrical products
  • Construction: Calculate material volumes for cylindrical structures
  • Packaging: Determine container volumes for shipping calculations

Tips for Accurate Measurements

  • Measure circumference carefully: Use a flexible measuring tape wrapped snugly around the cylinder
  • Ensure perpendicular measurement: The circumference should be measured at a right angle to the cylinder's length
  • Multiple measurements: Take several circumference measurements and use the average for better accuracy
  • Check units: Make sure all measurements use the same unit system before calculating