Relief Valve Sizing Calculator
Size pressure relief valves per API 520/526 for gas/vapor service. Calculates required orifice area and selects the standard API 526 orifice designation.
About this calculator
Sizes a pressure relief valve's required orifice area for gas/vapor service following API Standard 520 Part I's sizing methodology and the standard orifice designations (D through T) defined in API Standard 526. The calculator first converts the set pressure to the actual relieving pressure P1 by adding the overpressure allowance (10% is standard for a single valve, 16% for a fire case) plus atmospheric pressure, then converts relieving temperature to absolute (°R). It derives the gas-property coefficient C directly from the ratio of specific heats k using the API 520 formula C = 520·√(k·(2/(k+1))^((k+1)/(k-1))), which captures how easily the gas expands through the valve. Required orifice area then follows from mass flow rate, temperature, compressibility, C, the discharge coefficient (fixed at 0.975, the standard value for a certified conventional relief valve on vapor service), and molecular weight — heavier gases need less orifice area for the same mass flow because they carry more momentum per unit area.
The result is matched against the standard API 526 orifice letter sizes (D through T), selecting the smallest one that meets or exceeds the requirement, since valve manufacturers only build these fixed sizes rather than custom orifices. The tool also reports whether flow is critical (choked) by comparing the actual back-pressure ratio to the critical pressure ratio for the given k — nearly always true for a properly vented relief valve at low back-pressure. This is a screening-level API 520 calculation; a final relief valve selection should always be verified against the manufacturer's certified capacity and any back-pressure correction factors for balanced or pilot-operated valves.
Inputs
Results
Required orifice area (in²)
0.82
Selected API 526 orifice area (in²)
1.29
Figures current as of 2023. Sources: API Standard 520, Part I, 10th Edition (October 2020), American Petroleum Institute, API Standard 526, 8th Edition (August 2023), American Petroleum Institute
How to Use This Calculator
- Enter Mass flow rate W (lb/hr), Set pressure (psig), and Overpressure allowance (%).
- Set Back pressure (psia), Relieving temperature (°F), and Molecular weight (g/mol).
- Adjust Specific heat ratio k (Cp/Cv), Compressibility factor Z as needed.
- Review Required orifice area (in²) and Selected API 526 orifice area (in²).
- Use Required orifice area (mm²) and Relieving pressure P₁ (psia) to inform your decision.
How the result changes with Mass flow rate W (lb/hr)
| Mass flow rate W (lb/hr) | Required orifice area (in²) | Selected API 526 orifice area (in²) |
|---|---|---|
| 5,000 | 0.41 | 0.5 |
| 7,500 | 0.62 | 0.79 |
| 15,000 | 1.23 | 1.29 |
| 25,000 | 2.05 | 2.85 |
What each input means
- Mass flow rate W (lb/hr)
- Required relieving mass flow rate.
- Set pressure (psig)
- Valve set pressure (gauge).
- Overpressure allowance (%)
- Typically 10% for single valve, 16% for fire case.
- Back pressure (psia)
- Downstream pressure at valve outlet.
- Relieving temperature (°F)
- Temperature of the fluid at relieving conditions.
- Molecular weight (g/mol)
- Molecular weight of the gas (air = 28.97, methane = 16.04).
- Specific heat ratio k (Cp/Cv)
- Ratio of specific heats (air = 1.4, steam ≈ 1.33).
- Compressibility factor Z
- Gas compressibility (1.0 for ideal gas).
What each result means
- Required orifice area (in²)
- Minimum effective orifice area per API 520.
- Required orifice area (mm²)
- Same area in metric units.
- Selected API 526 orifice area (in²)
- Next standard orifice size that meets the requirement.
- Relieving pressure P₁ (psia)
- Set pressure plus overpressure plus atmospheric.
- Coefficient C
- Flow coefficient derived from specific heat ratio k.
- Critical pressure ratio
- Pressure ratio below which flow is critical (choked).
- Critical flow? (1=yes, 0=no)
- Whether flow through the valve is choked at these conditions.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersMass flow rate W (lb/hr) = 10000, Set pressure (psig) = 150, Overpressure allowance (%) = 10, Back pressure (psia) = 14.7 = 8 input(s) provided
- Calculate Required orifice areaRequired orifice area = (massFlow * sqrt(tempR * compressibility)) /0.8209 = 0.8209
- Calculate Selected API 526 orifice area1.287 = 1.287
- Calculate Required orifice areaRequired orifice area = areaIn2 * 645.16529.59 = 529.59
- Calculate Relieving pressure P₁Relieving pressure P₁ = setPressure * (1 + overpressurePct / 100) + 14.696179.7 = 179.7
Figures and sources
- API Std 520 Part I, Sizing, Selection, and Installation of Pressure-Relieving Devices — Part I: Sizing and Selection (2020) — API Standard 520, Part I, 10th Edition (October 2020), American Petroleum Institute
- API Std 526, Flanged Steel Pressure-Relief Valves (standard orifice designations D through T) (2023) — API Standard 526, 8th Edition (August 2023), American Petroleum Institute
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the calculator add both an overpressure allowance and atmospheric pressure to the set pressure?
A relief valve doesn't reach full rated capacity right at its set pressure — it needs to open further, which happens at the set pressure plus the accumulation/overpressure allowance (10% is standard for a single valve, 16% for a fire case). The calculator adds that percentage on top of set pressure, then adds 14.696 psi atmospheric to convert the gauge set pressure into the absolute relieving pressure P1 that the sizing equation requires.
Why does a heavier gas need a smaller orifice for the same mass flow?
The required area formula divides by the square root of molecular weight, so for identical mass flow rate, temperature, and pressure, a heavier gas (higher M) needs a smaller calculated orifice area. Physically, heavier gas molecules carry more momentum per unit area at a given mass flow rate, so less flow area is needed to pass the same mass through the valve.
Why does the tool round up to a letter like 'H' or 'J' instead of showing the exact area?
API 526 defines a fixed set of standard orifice sizes (D through T) that relief valve manufacturers actually build — there's no such thing as a custom orifice area in standard practice. The calculator reports the exact calculated area for reference, then separately selects the smallest standard letter designation whose area still meets or exceeds that requirement.
What does the critical flow check tell me?
It compares the actual back-pressure ratio (downstream pressure ÷ relieving pressure P1) to the critical pressure ratio derived from the gas's specific heat ratio k. When the actual ratio is at or below the critical ratio, flow through the valve is critical (choked), which is the condition the sizing formula assumes — it's nearly always true for a conventional relief valve venting to atmosphere or a low-pressure header.
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