Relief Valve Sizing Calculator (API 520 / API 526)

Relief valve sizing determines the orifice area a pressure relief valve (PSV) needs to discharge the required relieving rate at the relieving pressure. The method comes from API 520 Part I; the standardized orifice sizes come from API 526. Sizing is the third step of a four-step process: identify the overpressure scenarios (API 521), establish the governing relieving rate, compute the required area, and select the next-larger standard orifice.

Set pressure, overpressure, and relieving pressure

The valve is sized at the relieving pressure P1 — the set pressure plus the allowed overpressure, in absolute terms. ASME Section VIII permits 10% accumulation for a single valve in a non-fire case, 16% for multiple valves, and 21% for the external fire case; the overpressure selector above applies the matching factor to the set pressure.

Gas and vapor service

For critical (choked) flow — the usual case, whenever the back pressure is below roughly half the relieving pressure — the required area in SI units is:

• $A$ — required effective discharge area (mm²)
• $W$ — required relieving rate (kg/h)
• $C$ — coefficient from the specific-heat ratio k (≈ 0.027 for air)
• $P_1$ — relieving pressure (kPa absolute)
• $T, Z, M$ — temperature (K), compressibility, and molecular mass

When the back pressure is above the critical ratio, the flow is subcritical and the F2 method applies — the calculator switches automatically. For balanced-bellows valves, the back-pressure correction Kb from API 520 Figure 30 is used instead, up to 50% gauge back pressure.

Steam service

Steam sizing uses the Napier equation with two corrections: KN for set pressures above about 10.3 MPa, and the superheat correction KSH interpolated from the API 520 table (saturated steam has KSH = 1).

Liquid service

For liquid service with a certified valve, the SI form is:

• $Q$ — required relieving rate (L/min)
• $G$ — specific gravity relative to water
• $K_d, K_w, K_v$ — discharge coefficient (0.65), back-pressure correction (balanced valves), and viscosity correction from the Reynolds number
• $P_1 - P_2$ — relieving pressure minus total back pressure (kPa)

API 526 standard orifices

You do not buy an orifice of exactly the computed area: API 526 standardizes fourteen lettered orifice sizes from D (71 mm²) to T (16,774 mm²), and the next letter larger than the required area is selected. Resist adding margin by jumping extra letters — an oversized relief valve lifts, dumps more than the system supplies, slams shut, and repeats. That cycle is chatter, and it destroys seats.

Effective vs certified values

This calculator uses the API effective discharge coefficients (0.975 gas/steam, 0.65 liquid) with the API 526 effective areas — the preliminary-sizing system. The final check must use the manufacturer's actual orifice area together with its certified (National Board tested) discharge coefficient. Never mix one system's area with the other's coefficient.

What this calculator does not do

Two-phase and flashing-liquid relief is a specialist topic covered by API 520 Annex C and the DIERS methodology — none of the single-phase equations here may be extrapolated to it. Scenario determination (what governs: fire, blocked outlet, tube rupture…) and relieving-rate calculation per API 521 also sit upstream of this tool.

The two piping checks that make the valve work

A correctly sized valve is routinely wrecked by its piping. API 520 Part II limits the non-recoverable inlet-line loss to 3% of set pressure at rated flow — more, and the valve chatters. And the discharge flow creates built-up back pressure in the tailpipe: over 10% of set pressure, a conventional valve loses capacity and stability, which is what forces the switch to a balanced-bellows valve.

Both are ordinary compressible pressure-drop calculations on the inlet stub and tailpipe — exactly what a pipe network simulator answers.

For the full guide — terminology, certifications (ASME V/UV stamps, PED Category IV), and safe venting practice — see Safety Valve vs Relief Valve: Sizing & Certification Guide.

Related calculators & references

• Valve Cv/Kv sizing calculator
• Pipe friction loss calculator
• Steam table calculator

The standard's first sizing example, worked with the equations above: a hydrocarbon vapour relief of 24,270 kg/h at relieving pressure 670 kPa (absolute) and 348 K, M = 51, k = 1.11, Z = 0.90, discharging to atmosphere through a conventional valve (Kd = 0.975, Kb = Kc = 1).

1. Flow regime: back pressure over relieving pressure P2/P1 = 101.3/670 = 0.151; the critical-pressure ratio (2/(k+1))^(k/(k−1)) = 0.583. P2/P1 is less than the critical ratio, so the flow is critical (choked) and the back pressure does not enter the area.
2. Coefficient C = 0.03948 · √(k · (2/(k+1))^((k+1)/(k−1))) = 0.02489 (SI form: W in kg/h, P1 in kPa, A in mm²).
3. Required area A = W / (C · Kd · P1 · Kb · Kc) · √(T·Z/M) = 24,270 / (0.02489 × 0.975 × 670) · √(348 × 0.90 / 51) = 3,699 mm². The standard prints 3,698 mm² — its intermediate coefficients are rounded.
4. Orifice: the next-larger API 526 effective area is the P orifice, 4,116 mm², a 11.3 % capacity margin.
5. Example 2, subcritical: the same relief against 532 kPa (absolute) back pressure. P2/P1 = 0.794 exceeds 0.583, so the F2 method applies: F2 = 0.8548, A = 17.9 · W / (F2 · Kd · Kc) · √(T·Z / (M · P1 · (P1 − P2))) = 4,248 mm² (standard: 4,248).
6. Example 4, superheated steam: 69,615 kg/h at 707 K (813 °F) and 12,236 kPa (absolute). Napier with the high-pressure factor KN = 1.0115 and the superheat factor KSH = 0.855: A = 190.5 · W / (P1 · Kd · Kb · Kc · KN · KSH) = 1,285 mm² (standard: 1,285).
7. Example 5, liquid on a balanced valve: 1,800 US gpm of crude oil, G = 0.90, set 250 psig at 10 % overpressure, 50 psig back pressure (ΔP = 1,551 kPa). Back pressure is 20 % of set, so Kw = 0.9724 from the API 520 curve (the standard reads ≈ 0.97 off the figure); Kd = 0.65. First pass with Kv = 1: A = 3,059 mm² (standard: 3,066 — a 0.2 % rounding residual). The standard then checks the viscosity correction at the selected orifice, as the Liquid tab does automatically.

Regression summary — the standard's printed answers against this calculator, recomputed on every page load:

Small deviations come from the standard's own intermediate rounding (it works with rounded coefficients and unit conversions); the sizing functions are also verified term by term against the open-source fluids library's API 520 implementation.

These figures are computed by the same functions the tabs above run. To reproduce Example 1 on the Gas / Vapor tab: enter 24,270 kg/h and 348 with the K unit; switch the pressure field to Relieving Pressure (P1), select kPa(a) and enter 670 at 10 % overpressure; leave both back-pressure fields at their atmospheric defaults; pick a custom gas with M = 51, k = 1.11, Z = 0.90.