Annulus Calculator

How to Use the Annulus Calculator with Formulas

This Annulus Calculator allows you to perform various calculations related to the geometry of an annulus based on different input parameters. Below are instructions for each option available in the “Choose a Calculation” dropdown, including the relevant formulas.

1. Find C1, C2, A1, A2, A0 | Given r1, r2

• Inputs: Outer Radius (r1), Inner Radius (r2)
• Formulas:
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Outer Area $A1 = \pi \times r1^2$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• r1: 10 cm
• r2: 5 cm
• Results:
  • $C1 = 62.832 \, \text{cm}$
    
  • $C2 = 31.416 \, \text{cm}$
    
  • $A1 = 314.159 \, \text{cm}^2$
    
  • $A2 = 78.540 \, \text{cm}^2$
    
  • $A0 = 235.619 \, \text{cm}^2$
    

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2. Find r2, C1, A1, A2, A0 | Given r1, C2

• Inputs: Outer Radius (r1), Inner Circumference (C2)
• Formulas:
  • Inner Radius $r2 = \frac{C2}{2 \times \pi}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Outer Area $A1 = \pi \times r1^2$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• r1: 8 cm
• C2: 15 cm
• Results:
  • $r2 = 2.387 \, \text{cm}$
    
  • $C1 = 50.265 \, \text{cm}$
    
  • $A1 = 201.062 \, \text{cm}^2$
    
  • $A2 = 17.907 \, \text{cm}^2$
    
  • $A0 = 183.155 \, \text{cm}^2$
    

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3. Find r2, C1, C2, A1, A0 | Given r1, A2

• Inputs: Outer Radius (r1), Inner Area (A2)
• Formulas:
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Outer Area $A1 = \pi \times r1^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• r1: 10 cm
• A2: 50 cm²
• Results:
  • $r2 = 3.989 \, \text{cm}$
    
  • $C1 = 62.832 \, \text{cm}$
    
  • $C2 = 25.064 \, \text{cm}$
    
  • $A1 = 314.159 \, \text{cm}^2$
    
  • $A0 = 264.159 \, \text{cm}^2$
    

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4. Find r1, C2, A1, A2, A0 | Given r2, C1

• Inputs: Inner Radius (r2), Outer Circumference (C1)
• Formulas:
  • Outer Radius $r1 = \frac{C1}{2 \times \pi}$
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Outer Area $A1 = \pi \times r1^2$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• r2: 3 cm
• C1: 31.4159 cm
• Results:
  • $r1 = 5 \, \text{cm}$
    
  • $C2 = 18.85 \, \text{cm}$
    
  • $A1 = 78.540 \, \text{cm}^2$
    
  • $A2 = 28.274 \, \text{cm}^2$
    
  • $A0 = 50.265 \, \text{cm}^2$
    

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5. Find r1, r2, A1, A2, A0 | Given C1, C2

• Inputs: Outer Circumference (C1), Inner Circumference (C2)
• Formulas:
  • Outer Radius $r1 = \frac{C1}{2 \times \pi}$
  • Inner Radius $r2 = \frac{C2}{2 \times \pi}$
  • Outer Area $A1 = \pi \times r1^2$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• C1: 50 cm
• C2: 20 cm
• Results:
  • $r1 = 7.96 \, \text{cm}$
    
  • $r2 = 3.18 \, \text{cm}$
    
  • $A1 = 199.65 \, \text{cm}^2$
    
  • $A2 = 31.79 \, \text{cm}^2$
    
  • $A0 = 167.86 \, \text{cm}^2$
    

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6. Find r1, r2, C2, A1, A0 | Given C1, A2

• Inputs: Outer Circumference (C1), Inner Area (A2)
• Formulas:
  • Outer Radius $r1 = \frac{C1}{2 \times \pi}$
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Outer Area $A1 = \pi \times r1^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• C1: 62.832 cm
• A2: 28 cm²
• Results:
  • $r1 = 10 \, \text{cm}$
  • $r2 = 2.989 \, \text{cm}$
  • $C2 = 18.791 \, \text{cm}$
  • $A1 = 314.159 \, \text{cm}^2$
  • $A0 = 286.159 \, \text{cm}^2$

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7. Find r1, C1, C2, A2, A0 | Given r2, A1

• Inputs: Inner Radius (r2), Outer Area (A1)
• Formulas:
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• r2: 4 cm
• A1: 100 cm²
• Results:
  • $r1 = 5.641 \, \text{cm}$
    
  • $C1 = 35.444 \, \text{cm}$
    
  • $C2 = 25.133 \, \text{cm}$
    
  • $A2 = 50.265 \, \text{cm}^2$
    
  • $A0 = 49.735 \, \text{cm}^2$
    

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8. Find r1, r2, C1, A2, A0 | Given C2, A1

• Inputs: Inner Circumference (C2), Outer Area (A1)
• Formulas:
  • Inner Radius $r2 = \frac{C2}{2 \times \pi}$
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Area $A2 = \pi \times r2^2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• C2: 31.416 cm
• A1: 314.159 cm²
• Results:
  • $r2 = 5 \, \text{cm}$
    
  • $r1 = 10 \, \text{cm}$
    
  • $C1 = 62.832 \, \text{cm}$
    
  • $A2 = 78.54 \, \text{cm}^2$
    
  • $A0 = 235.619 \, \text{cm}^2$
    

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9. Find r1, r2, C1, C2, A0 | Given A1, A2

• Inputs: Outer Area (A1), Inner Area (A2)
• Formulas:
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Annulus Area $A0 = A1 – A2 = \pi \times (r1^2 – r2^2)$
    

Example:

• A1: 314.159 cm²
• A2: 78.54 cm²
• Results:
  • $r1 = 10 \, \text{cm}$
    
  • $r2 = 5 \, \text{cm}$
    
  • $C1 = 62.832 \, \text{cm}$
    
  • $C2 = 31.416 \, \text{cm}$
    
  • $A0 = 235.619 \, \text{cm}^2$
    

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10. Find r2, C1, C2, A2, A0 | Given r1, A0

• Inputs: Outer Radius (r1), Annulus Area (A0)
• Formulas:
  • Inner Area $A2 = \pi \times r1^2 – A0$
    
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Outer Area $A1 = \pi \times r1^2$
    

Example:

• r1: 10 cm
• A0: 200 cm²
• Results:
  • $A2 = 114.159 \, \text{cm}^2$
    
  • $r2 = 6.035 \, \text{cm}$
    
  • $C1 = 62.832 \, \text{cm}$
    
  • $C2 = 37.917 \, \text{cm}$
    
  • $A1 = 314.159 \, \text{cm}^2$
    

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11. Find r1, C1, C2, A1, A2 | Given r2, A0

• Inputs: Inner Radius (r2), Annulus Area (A0)
• Formulas:
  • Outer Area $A1 = A0 + \pi \times r2^2$
    
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    
  • Inner Area $A2 = \pi \times r2^2$
    

Example:

• r2: 5 cm
• A0: 150 cm²
• Results:
  • $A1 = 228.54 \, \text{cm}^2$
    
  • $r1 = 8.533 \, \text{cm}$
    
  • $C1 = 53.594 \, \text{cm}$
    
  • $C2 = 31.416 \, \text{cm}$
    
  • $A2 = 78.54 \, \text{cm}^2$
    

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12. Find r1, r2, C2, A1, A2 | Given C1, A0

• Inputs: Outer Circumference (C1), Annulus Area (A0)
• Formulas:
  • Outer Radius $r1 = \frac{C1}{2 \times \pi}$
  • Outer Area $A1 = \pi \times r1^2$
    
  • Inner Area $A2 = A1 – A0$
    
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    

Example:

• C1: 62.832 cm
• A0: 150 cm²
• Results:
  • $r1 = 10 \, \text{cm}$
    
  • $A1 = 314.159 \, \text{cm}^2$
    
  • $A2 = 164.159 \, \text{cm}^2$
    
  • $r2 = 7.231 \, \text{cm}$
    
  • $C2 = 45.429 \, \text{cm}$
    

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13. Find r1, r2, C1, A1, A2 | Given C2, A0

• Inputs: Inner Circumference (C2), Annulus Area (A0)
• Formulas:
  • Inner Radius $r2 = \frac{C2}{2 \times \pi}$
  • Inner Area $A2 = \pi \times r2^2$
    
  • Outer Area $A1 = A0 + A2$
    
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    

Example:

• C2: 31.416 cm
• A0: 150 cm²
• Results:
  • $r2 = 5 \, \text{cm}$
    
  • $A2 = 78.54 \, \text{cm}^2$
    
  • $A1 = 228.54 \, \text{cm}^2$
    
  • $r1 = 8.533 \, \text{cm}$
    
  • $C1 = 53.594 \, \text{cm}$
    

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14. Find r1, r2, C1, C2, A2 | Given A1, A0

• Inputs: Outer Area (A1), Annulus Area (A0)
• Formulas:
  • Inner Area $A2 = A1 – A0$
    
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    

Example:

• A1: 314.159 cm²
• A0: 150 cm²
• Results:
  • $A2 = 164.159 \, \text{cm}^2$
    
  • $r1 = 10 \, \text{cm}$
    
  • $r2 = 7.231 \, \text{cm}$
    
  • $C1 = 62.832 \, \text{cm}$
    
  • $C2 = 45.429 \, \text{cm}$
    

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15. Find r1, r2, C1, C2, A1 | Given A2, A0

• Inputs: Inner Area (A2), Annulus Area (A0)
• Formulas:
  • Outer Area $A1 = A0 + A2$
    
  • Inner Radius $r2 = \sqrt{\frac{A2}{\pi}}$
  • Outer Radius $r1 = \sqrt{\frac{A1}{\pi}}$
  • Outer Circumference $C1 = 2 \times \pi \times r1$
    
  • Inner Circumference $C2 = 2 \times \pi \times r2$
    

Example:

• A2: 78.54 cm²
• A0: 150 cm²
• Results:
  • $A1 = 228.54 \, \text{cm}^2$
    
  • $r2 = 5 \, \text{cm}$
    
  • $r1 = 8.533 \, \text{cm}$
    
  • $C1 = 53.594 \, \text{cm}$
    
  • $C2 = 31.416 \, \text{cm}$