Annulus Calculator
This online tool finds areas, circumferences and radii of an annulus. Enter two known quantities below and select the calculation mode to compute the remaining values. Visual 3D ring updates in real time.
Interactive 3D preview
Rotate: drag • Zoom: mouse wheel / pinch • Click Calculate to update
Choose known variables
Pi value and precision below
Annulus Formulas & Definitions
r1 = outer radius
r2 = inner radius
C1 = outer circumference
C2 = inner circumference
A1 = area of circle of r1, area within outer circle
A2 = area of circle of r2, area within inner circle
A0 = shaded area, outer area minus inner area
A0 = A1 - A2
π = pi = 3.1415926535898
√ = square root
This online calculator will find the area, circumference and radii of an annulus. With any 2 known variables you can calculate the other 5 unknowns. Use the following formulas and sets of equations below to calculate measures of an annulus.
Area of the annulus A0 = A1 - A2 = π(r1² - r2²).
Outer circumference C1 = 2πr1. Inner circumference C2 = 2πr2.
Outer area A1 = π r1². Inner area A2 = π r2².
Sets of formulas used in calculations are applied depending on which two values you input.
r2 = inner radius
C1 = outer circumference
C2 = inner circumference
A1 = area of circle of r1, area within outer circle
A2 = area of circle of r2, area within inner circle
A0 = shaded area, outer area minus inner area
A0 = A1 - A2
π = pi = 3.1415926535898
√ = square root
This online calculator will find the area, circumference and radii of an annulus. With any 2 known variables you can calculate the other 5 unknowns. Use the following formulas and sets of equations below to calculate measures of an annulus.
Area of the annulus A0 = A1 - A2 = π(r1² - r2²).
Outer circumference C1 = 2πr1. Inner circumference C2 = 2πr2.
Outer area A1 = π r1². Inner area A2 = π r2².
Sets of formulas used in calculations are applied depending on which two values you input.
| Given | Compute |
|---|---|
| r1, r2 | C1, C2, A1, A2, A0 |
| C1, C2 | r1, r2, A1, A2, A0 |
| A1, A2 | r1, r2, C1, C2, A0 |
outer radius (r1)
—
inner radius (r2)
—
outer circumference (C1)
—
inner circumference (C2)
—
outer circle area (A1)
—
inner circle area (A2)
—
annulus area (A0)
—
Annulus Calculations & Methods (full reference)
The area of the annulus between r1 and r2, the shaded area, is the area contained by the outer circle minus the area contained by the inner circle or A0 = A1 - A2. You will need to know 2 elements in order to calculate the remaining variables.
Annulus Formulas in terms of radius r and π
Outer circumference of an annulus: C1 = 2πr1
Inner circumference of an annulus: C2 = 2πr2
Surface area of the space enclosed by the outer circle: A1 = π r1²
Surface area of the space enclosed by the inner circle: A2 = π r2²
Surface area of the annulus (the shaded area): A0 = A1 - A2 = π(r1² - r2²)
All the calculation sets shown in the classic reference are implemented. Use the dropdown to select how you'd like to supply the two known values and click Calculate. The 3D visualization will update to match your radii, and the numeric outputs will show the computed results (rounded to the significant figures you selected).
Annulus Formulas in terms of radius r and π
Outer circumference of an annulus: C1 = 2πr1
Inner circumference of an annulus: C2 = 2πr2
Surface area of the space enclosed by the outer circle: A1 = π r1²
Surface area of the space enclosed by the inner circle: A2 = π r2²
Surface area of the annulus (the shaded area): A0 = A1 - A2 = π(r1² - r2²)
All the calculation sets shown in the classic reference are implemented. Use the dropdown to select how you'd like to supply the two known values and click Calculate. The 3D visualization will update to match your radii, and the numeric outputs will show the computed results (rounded to the significant figures you selected).