BIZOMAT MAKEOS · Springs
Relief Valve Spring Check (Cracking Pressure, Full-Lift Pressure, Overpressure, Spring Stress)
For a direct-acting relief or check valve held shut by a coil spring, what pressure does it crack at, how much higher is it at full lift, and is the spring stressed within limits?
Check of the spring of a direct-acting poppet or ball relief valve: the spring rate, installed load and shear stress at the closed length (as the compression spring tool), the cracking pressure from the installed load over the seat area, the pressure at full lift from the extra spring load, the overpressure (accumulation) between them, the stress at full lift and the clearance to solid, against the set pressure and tolerance wanted, the allowed overpressure and the allowable stress.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Seat diameter (sealing) | mm | Diameter of the seat where the poppet or ball seals (the area the pressure acts on). |
| Full lift of the poppet | mm | How far the poppet opens at full flow. |
| Set pressure wanted | MPa | Pressure the valve should start to open at. |
| Set pressure tolerance (±) | % | How far the cracking pressure may be from the wanted pressure. |
| Largest overpressure at full lift | % | Largest rise above cracking pressure allowed at full lift. |
| Spring | ||
| Wire diameter | mm | Wire diameter. |
| Mean coil diameter | mm | Mean coil diameter. |
| Active coils | coils | Active coils. |
| End type | choice | End type of the spring. |
| Shear modulus | GPa | Shear modulus of the spring wire. |
| Unloaded length | mm | Length of the spring with no load. |
| Installed length (valve shut) | mm | Length of the spring fitted in the valve with the valve shut. |
| Allowable shear stress | MPa | Allowable shear stress for the spring wire and duty. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Seat diameter (sealing)
- What it is
- The diameter of the circle where the poppet or ball seals on the seat. Pressure acts on the area inside it to lift the poppet against the spring.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cracking pressure falls with the square of the seat diameter for the same spring load.
- Get it right
- Use the sealing contact diameter, not the bore below the seat or the poppet’s outside diameter.
What this means: Full lift of the poppet
- What it is
- How far the poppet or ball moves off its seat when the valve passes full flow. The spring is compressed by this extra amount at full lift.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More lift raises the full-lift pressure, the overpressure and the spring stress.
- Get it right
- Use the lift needed for the rated flow, from the valve design or maker.
What this means: Set pressure wanted
- What it is
- The pressure at which the valve is wanted to start opening (cracking pressure), compared with the pressure worked out from the spring’s installed load.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.9 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in MPa: 1 bar = 0.1 MPa. Use gauge pressure if the spring side of the poppet is at atmosphere.
What this means: Set pressure tolerance (±)
- What it is
- How far the cracking pressure may differ from the wanted set pressure, as a plus-or-minus share of the set pressure.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 50%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself, not a fraction; take it from the system specification.
What this means: Largest overpressure at full lift
- What it is
- The largest rise above the cracking pressure allowed when the valve is at full lift, as a share of the cracking pressure (also called accumulation).
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 200%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself; take the limit from the system or code that governs the valve.
Spring
What this means: Wire diameter
- What it is
- The diameter of the spring wire.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate, and so the installed load and cracking pressure, rise with the fourth power of wire diameter, so small changes matter.
- Get it right
- Measure the wire with a micrometer; it has a very strong effect on rate and stress.
What this means: Mean coil diameter
- What it is
- The mean coil diameter: the outside coil diameter minus one wire diameter, measured to the centre of the wire.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate falls with the cube of the mean diameter.
- Get it right
- Do not enter the outside diameter: subtract one wire diameter from it first.
What this means: Active coils
- What it is
- The number of coils that are free to deflect, excluding the dead coils closed at each end.
- Units and format
- Enter a number in coils: a number of coils. The form accepts 0.5 coils to 10000 coils. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 coils as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate falls in proportion as active coils increase.
- Get it right
- Total coils include the end coils; for closed ends the tool takes the total as active coils plus two.
What this means: End type
- What it is
- How the spring ends are finished. The tool uses it to work out the total coils and the solid length, which is checked against the length at full lift.
- Units and format
- Choose one of 4 options from the list: Closed and ground (squared and ground); Closed, not ground; Plain and ground; Plain (open).
- Example
- The form opens with “Closed and ground (squared and ground)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Check the drawing or the spring itself; ground ends sit flat and give a shorter solid length.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the spring wire material, used to work out the spring rate.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 79.3 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate rises in proportion to it.
- Get it right
- Enter it in GPa, not MPa; take it from the spring wire supplier’s data.
What this means: Unloaded length
- What it is
- The length of the spring standing free with no load, its free length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer free length gives more installed load and a higher cracking pressure.
- Get it right
- Measure it on the actual spring; springs can take a set after first loading.
What this means: Installed length (valve shut)
- What it is
- The length of the spring as fitted in the valve with the poppet shut on its seat. The installed load is the spring rate times free length minus this length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter installed length raises the installed load and the cracking pressure.
- Get it right
- It must not exceed the free length; shims or an adjusting screw change it.
What this means: Allowable shear stress
- What it is
- The highest shear stress you allow in the spring wire, compared with the stress at full lift.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the spring wire supplier or a spring design standard for your wire, size and duty.
Method and formulas
- k = G d⁴ ÷ (8 D³ N_a); load F = k (L₀ − L); τ = K 8 F D ÷ (π d³) with the Wahl factor (as the compression spring tool).
- Seat area A = π d_s² ÷ 4; cracking pressure = F_installed ÷ A; full-lift pressure = k (L₀ − L_w + lift) ÷ A.
- Overpressure = full-lift ÷ cracking − 1; length at full lift against the solid length.
- Example: cracks at 0.92439 MPa, 1.0168 MPa at full lift (10% over); 481.58 MPa in the spring.
Limitations
- Static balance on the seat area; flow forces on an open poppet change the full-lift pressure.
- Spring at room temperature; hot oil lowers G slightly.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the spring for a small relief or check valve
- Find why a relief valve chatters or overpressures
- Re-shim a valve to a new set pressure
Who it is for
- Hydraulic engineers
- Valve designers
- Maintenance engineers
What you get
- Spring rate, installed load and stress
- Cracking and full-lift pressure, overpressure
- Checks against the set pressure, stress and solid
Interpreting the result
- A softer spring (more coils) cuts the overpressure but needs more installed compression for the same set pressure.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–324. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Springs that set a force: detents, relief valves and spring-applied clamps
What it covers: How springs set forces and pressures in machines: ball detent release force, relief valve cracking pressure and overpressure, spring-applied hydraulic release clamps, and records.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.