Barlow Formula Calculator
Find pipe design pressure from diameter, wall, strength, and design factors.
What it does
The Barlow formula links the pressure inside a pipe to the pipe's diameter, wall thickness, and material strength. It is a thin-wall approximation, but it is the starting point for many pipeline and pressure vessel rules.
This calculator gives two pressures. The Barlow pressure at yield is 2St/D, where S is the yield strength, t is the wall thickness, and D is the nominal outside diameter. The design pressure multiplies that value by a design factor F, a longitudinal joint factor E, and a temperature derating factor T.
The defaults describe a 12 in outside diameter pipe with a 0.25 in wall and a 35,000 psi yield strength. The Barlow pressure is 1,458.3 psi. With F = 0.72, E = 1.0, and T = 1.0, the design pressure is 1,050.0 psi. The same inputs in metric give 10.055 MPa at yield and 7.239 MPa for design.
The design factors are not universal. A gas transmission line may use 0.72 in a Class 1 location and lower values in more populated areas. Welded pipe may need a joint factor below 1.0. High temperatures may need a temperature factor below 1.0. Use the values from the code that governs your project, not the defaults on this page.
How to use
- Pick imperial or metric. The diameter, wall, and strength fields change with the system.
- Enter the nominal outside diameter and the nominal wall thickness.
- Enter the specified minimum yield strength for the pipe grade.
- Enter the design factor F, the longitudinal joint factor E, and the temperature factor T from the governing code.
- Read the design pressure first, then compare it with the Barlow pressure at yield.
- Check the D/t ratio. Below 20, the thin-wall assumption is weaker and a thick-wall method may be needed.
Formula
- P_barlow
- Internal pressure at yield from the basic Barlow formula.
- P_design
- Allowable design pressure after factors.
- S
- Specified minimum yield strength of the pipe material.
- t
- Nominal wall thickness.
- D
- Nominal outside diameter.
- F
- Design factor from the governing code.
- E
- Longitudinal joint factor.
- T
- Temperature derating factor.
The formula uses the outside diameter, not the inside diameter. It assumes a thin wall, a circular section, and a pressure well below the burst pressure. The design pressure is the basic Barlow pressure multiplied by F, E, and T. If the pipe has a corrosion allowance or a future wall loss, use the remaining wall in the calculation or follow the code's remaining strength method.
Worked example
Example: 12 in pipe with a 0.25 in wall
Defaults: 12 in outside diameter, 0.25 in wall, 35,000 psi yield, F = 0.72, E = 1.0, T = 1.0.
- Basic Barlow pressure: 2 x 35,000 x 0.25 / 12 = 1,458.3 psi.
- Design pressure: 1,458.3 x 0.72 x 1.0 x 1.0 = 1,050.0 psi.
- Allowable hoop stress: 35,000 x 0.72 x 1.0 x 1.0 = 25,200 psi.
- Diameter to wall ratio: 12 / 0.25 = 48.
- Metric defaults: 304.8 mm outside diameter, 6.35 mm wall, and 241.3165 MPa yield give 10.055 MPa at yield, 7.239 MPa for design, 173.75 MPa allowable hoop stress, and a D/t of 48.
- The tool shows 1,050.0 psi, 1,458.3 psi, 25,200.0 psi, and 48.0 in imperial, or 7.239 MPa, 10.055 MPa, 173.75 MPa, and 48.0 in metric.
Reference table
| Grade | Yield strength | F, E, T | Design pressure |
|---|---|---|---|
| Grade B | 35,000 psi | 0.72, 1.0, 1.0 | 1,050.0 psi |
| Grade B | 35,000 psi | 0.60, 1.0, 1.0 | 875.0 psi |
| X42 | 42,000 psi | 0.72, 1.0, 1.0 | 1,260.0 psi |
| X52 | 52,000 psi | 0.72, 0.8, 1.0 | 1,248.0 psi |
| X60 | 60,000 psi | 0.72, 1.0, 0.9 | 1,620.0 psi |
Limits
- Thin-wall approximation. The usual range is D/t of 20 or more. Below that, use a thick-wall formula.
- Uses the nominal outside diameter and nominal wall. Corrosion, mill tolerance, and future wall loss need a separate check.
- The design factors are inputs, not recommendations. The governing code sets F, E, and T.
- Does not check external pressure, bending, fatigue, supports, fittings, or thermal expansion.
Common mistakes
- Using the inside diameter instead of the outside diameter.
- Multiplying by the design factor twice.
- Using tensile strength where the code requires yield strength.
- Applying a joint factor of 1.0 to a welded pipe without checking the code.
- Ignoring corrosion allowance or wall loss in an existing pipe.
Try it yourself
Quick checks. Answers sit tucked under each question.
An 8.625 in OD pipe has a 0.322 in wall and 35,000 psi yield. F is 0.72, E is 1.0, and T is 1.0. What is the design pressure?
Basic pressure is 2,613.3 psi. Design pressure is 1,881.6 psi. The D/t ratio is 26.79.
A 12 in OD pipe has a 0.375 in wall and 42,000 psi yield. F is 0.60, E is 0.8, and T is 1.0. What is the design pressure?
Basic pressure is 2,625.0 psi. Design pressure is 1,260.0 psi. The D/t ratio is 32.0.
Using the metric defaults, what is the design pressure with F = 0.72, E = 1.0, and T = 1.0?
2 x 241.3165 x 6.35 / 304.8 = 10.055 MPa at yield. Multiplying by 0.72 gives 7.239 MPa.
Questions
What does the Barlow formula calculate?
It estimates the internal pressure at which the hoop stress in a thin pipe wall reaches the material's yield strength. Multiplying by design factors gives an allowable design pressure.
Should I use outside or inside diameter?
The common Barlow form uses the nominal outside diameter. Some references use the inside or mean diameter. Use the definition in the code that governs your work and apply it consistently.
What is a typical design factor for a gas pipeline?
In the United States, 49 CFR 192.105 uses 0.72 for Class 1 locations and lower values for Classes 2, 3, and 4. The class depends on the number of buildings near the line.
Why is the joint factor less than 1?
A longitudinal weld can be weaker than the base metal. The code assigns a joint factor based on the weld type and inspection. Seamless pipe often uses 1.0.
Can I use Barlow for a pressure vessel?
It is a starting estimate for thin walls, but pressure vessel codes use their own design equations and factors. Do not substitute this page for a code design.
What if D/t is below 20?
The thin-wall assumption becomes weaker. The hoop stress is no longer close to uniform through the wall. Use a thick-wall formula such as Lame's equations or a qualified engineer.
Sources
- 49 CFR 192.105: Design formula for steel pipe
- University of Washington: Thin walled pressure vessels