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Hoop Stress Calculator.

Calculate thin-wall pressure-vessel hoop stress.

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Internal pressure

Radius

Wall thickness

Hoop stress

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Educational SI models with assumptions stated in each description; verify engineering decisions independently.

Use Cases

Pressure vessel design

Engineers use hoop stress calculations to ensure that pipes, tanks, and boilers can safely withstand internal pressure without yielding or bursting.

Example: Designing a compressed air tank with 1 MPa pressure, 0.5 m radius, and 5 mm wall thickness.

Material selection

By comparing calculated hoop stress to material yield strength, engineers can choose appropriate materials and thicknesses for safe operation.

Example: Checking if a steel pipe can handle 2 MPa pressure with a 0.3 m radius and 3 mm wall.

Frequently Asked Questions

What is hoop stress?: Hoop stress is the circumferential stress in a cylindrical or spherical pressure vessel wall caused by internal pressure. It acts tangentially to the circumference and is a key factor in vessel design.
How is hoop stress calculated?: For a thin-walled vessel, hoop stress is calculated as (Internal pressure × Radius) / Wall thickness. This formula assumes uniform stress distribution and wall thickness much smaller than the radius.
What is the thin-wall assumption?: The thin-wall assumption applies when the wall thickness is less than about one-tenth of the radius. It simplifies stress analysis by ignoring radial stress variations, making the formula accurate for most practical vessels.

Tips & Common Mistakes

Tips

Ensure all units are consistent: use Pascals for pressure, meters for radius and thickness.
Verify that the wall thickness is less than 10% of the radius to apply the thin-wall formula accurately.
For thick-walled vessels, use Lame's equation instead, as this calculator is only for thin walls.
Double-check your radius measurement: it should be the inner radius, not the outer diameter.

Common Mistakes to Avoid

Using diameter instead of radius in the formula, which doubles the stress value incorrectly.
Mixing units, such as using bar for pressure and mm for dimensions without converting to Pa and m.
Applying the thin-wall formula to thick-walled vessels where stress distribution is not uniform.

Last updated: August 13, 2026

Use Cases

Pressure vessel design

Engineers use hoop stress calculations to ensure that pipes, tanks, and boilers can safely withstand internal pressure without yielding or bursting.

Example: Designing a compressed air tank with 1 MPa pressure, 0.5 m radius, and 5 mm wall thickness.

Material selection

By comparing calculated hoop stress to material yield strength, engineers can choose appropriate materials and thicknesses for safe operation.

Example: Checking if a steel pipe can handle 2 MPa pressure with a 0.3 m radius and 3 mm wall.

Frequently Asked Questions

What is hoop stress?

Hoop stress is the circumferential stress in a cylindrical or spherical pressure vessel wall caused by internal pressure. It acts tangentially to the circumference and is a key factor in vessel design.

How is hoop stress calculated?

For a thin-walled vessel, hoop stress is calculated as (Internal pressure × Radius) / Wall thickness. This formula assumes uniform stress distribution and wall thickness much smaller than the radius.

What is the thin-wall assumption?

The thin-wall assumption applies when the wall thickness is less than about one-tenth of the radius. It simplifies stress analysis by ignoring radial stress variations, making the formula accurate for most practical vessels.

Tips & Common Mistakes

Tips

Ensure all units are consistent: use Pascals for pressure, meters for radius and thickness.
Verify that the wall thickness is less than 10% of the radius to apply the thin-wall formula accurately.
For thick-walled vessels, use Lame's equation instead, as this calculator is only for thin walls.
Double-check your radius measurement: it should be the inner radius, not the outer diameter.

Common Mistakes to Avoid

Using diameter instead of radius in the formula, which doubles the stress value incorrectly.
Mixing units, such as using bar for pressure and mm for dimensions without converting to Pa and m.
Applying the thin-wall formula to thick-walled vessels where stress distribution is not uniform.

Use Cases

Pressure vessel design

Engineers use hoop stress calculations to ensure that pipes, tanks, and boilers can safely withstand internal pressure without yielding or bursting.

Example: Designing a compressed air tank with 1 MPa pressure, 0.5 m radius, and 5 mm wall thickness.

Material selection

By comparing calculated hoop stress to material yield strength, engineers can choose appropriate materials and thicknesses for safe operation.

Example: Checking if a steel pipe can handle 2 MPa pressure with a 0.3 m radius and 3 mm wall.

Frequently Asked Questions

What is hoop stress?

How is hoop stress calculated?

What is the thin-wall assumption?

Tips & Common Mistakes

Tips

Ensure all units are consistent: use Pascals for pressure, meters for radius and thickness.
Verify that the wall thickness is less than 10% of the radius to apply the thin-wall formula accurately.
For thick-walled vessels, use Lame's equation instead, as this calculator is only for thin walls.
Double-check your radius measurement: it should be the inner radius, not the outer diameter.

Common Mistakes to Avoid

Using diameter instead of radius in the formula, which doubles the stress value incorrectly.
Mixing units, such as using bar for pressure and mm for dimensions without converting to Pa and m.
Applying the thin-wall formula to thick-walled vessels where stress distribution is not uniform.