Geometry Tool

Annulus Calculator

Calculate the area, width, and perimeter of a ring (the area between two concentric circles).

Σ The Formula

Area = π(R² - r²)

Real World Examples

Large Ring
Outer Radius: 10, Inner Radius: 5 → Area: 235.62
Washers
Outer Radius: 5mm, Inner Radius: 2mm → Area: 65.97mm²

# About This Calculator

An annulus is a geometric shape representing the region between two concentric circles. It looks like a ring, a washer, or a donut (when viewed from above).

The key parameters of an annulus are its Outer Radius (R) and Inner Radius (r). These are used to determine the surface area of the ring itself, excluding the hole in the middle.

Annuli are common in engineering (calculating the surface area of seals, gaskets, and pipes), architecture (designing circular plazas or walkways), and astronomy (describing the rings of planets or the shape of an annular eclipse).

How To Use

  1. Enter the **Outer Radius (R)** of the large circle.
  2. Enter the **Inner Radius (r)** of the small circle (the hole).
  3. Click **Calculate** to find the area, total perimeter, and width of the ring.

Frequently Asked Questions

Can the inner radius be larger than the outer radius?+

No. For a ring to exist, the outer circle must be larger than the inner one. If they are equal, the area is zero.

What is the perimeter of an annulus?+

In geometry, the perimeter of an annulus is typically the sum of the circumferences of both the inner and outer circles, as both 'edges' define its boundary.

How do I calculate the volume of a 3D ring?+

A 3D annulus is called a Torus. To find its volume, you would multiply the cross-sectional area of the ring by the circumference of the circle formed by the center of the ring's tube.

Is Annulus Calculator free to use?+

Yes, Annulus Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

How accurate is Annulus Calculator?+

We use standard mathematical formulas and high-precision computing algorithms to ensure results for Annulus Calculator are accurate for academic and professional use.

Can I use Annulus Calculator on my phone?+

Yes! Annulus Calculator is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.

About

An annulus is a geometric shape representing the region between two concentric circles. It looks like a ring, a washer, or a donut (when viewed from above).

The key parameters of an annulus are its Outer Radius (R) and Inner Radius (r). These are used to determine the surface area of the ring itself, excluding the hole in the middle.

Annuli are common in engineering (calculating the surface area of seals, gaskets, and pipes), architecture (designing circular plazas or walkways), and astronomy (describing the rings of planets or the shape of an annular eclipse).

Related Tools

Capsule Calc

Volume Calculator

Surface Area

Pythagorean