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H₂ mass calculator
How much hydrogen is really in that tank? At 700 bar the ideal gas law overshoots by almost half — this calculator uses NIST real-gas data instead. Enter any three of pressure, volume, temperature and mass; it solves the fourth.
SOLVE FOR
PRESET
HYDROGEN MASS
6.993kg
The ideal gas law would claim 10.25 kg — 46.6 % more than is really in there (Z = 1.466).
+10 °C → −2.3 % mass
Compressibility data: NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP). Valid domain: −125…125 °C, 1…1000 bar (abs). Educational tool — not a substitute for certified metering.
How it works — physics, data sources, scope
Why the ideal gas law is not enough. PV = nRT assumes volumeless molecules that never interact. At 700 bar their own size and short-range repulsion matter, and fewer fit into the tank than the ideal law predicts. The correction is the measured compressibility factor Z: m = P·V·M / (Z(T,P)·R·T) — for hydrogen at 700 bar and 15 °C, Z ≈ 1.47.
Why the error always goes the same way. In this whole domain hydrogen sits far above its Boyle temperature (≈ −163 °C), so repulsion dominates and Z > 1 throughout. The ideal law therefore always claims more hydrogen than is really there — the dangerous direction for storage sizing, trailer logistics or billing.
Where the ideal gas law is still fine. The overestimate at 15 °C, straight from the NIST data: +0.6 % at 10 bar, +23 % at 350 bar (bus and truck systems), +47 % at 700 bar (passenger cars), +67 % at 1000 bar (dispenser supply). Below ~20 bar the ideal law stays within about one percent; above ~100 bar a real-gas model is non-negotiable.
How this calculator computes it. Z(T, P) is bilinearly interpolated from the NIST REFPROP table (−125…125 °C, 1…1000 bar); the test suite cross-checks against NIST's independent density table at 77 grid points (within ±0.2 %). Solving for temperature or pressure inverts the same relation by bisection; inputs outside the domain are reported as such, never silently clamped.
One practical trap: gauge vs absolute pressure. Gauges read relative to the atmosphere; the physics needs absolute pressure. The abs/gauge toggle handles the 1.013 bar offset — negligible at 700 bar, a real error source in low-pressure work.
FREQUENTLY ASKED QUESTIONS
How much hydrogen fits in a 700 bar tank?
A typical passenger-car tank of 174 L holds about 7.0 kg of hydrogen at 700 bar and 15 °C — calculated with real-gas data from NIST. The ideal gas law would claim over 10 kg: at that pressure it overestimates by about 47 %.
Why is the ideal gas law wrong for hydrogen at high pressure?
Hydrogen at these conditions is far above its Boyle temperature, so molecular repulsion dominates and the compressibility factor is greater than one — Z ≈ 1.47 at 700 bar and 15 °C. The ideal gas law ignores this and always predicts more hydrogen than is really in the tank: about +23 % at 350 bar, +47 % at 700 bar.
When is the ideal gas law still good enough for hydrogen?
Below roughly 20 bar the error stays within about one percent — fine for low-pressure piping estimates. Above ~100 bar it passes the few-percent mark and grows nearly linearly with pressure, so at vehicle refueling pressures a real-gas model is mandatory.