Calculate hydrogen buoyant lift or required gas volume from temperature, pressure, purity, envelope mass, and payload, with density and helium comparison details.

Enter gas volume at the modeled ambient conditions.

Hydrogen is highly flammable. This is a buoyancy estimate, not a safe-mixture or handling guide. Ideal gases share ambient temperature and absolute pressure. Defaults:15°C,101.325 kPa,100% hydrogen; blank envelope mass means0.

Optional settings

Blank means0. Exclude lifting gas; its mass is already accounted for.

Remainder is modeled as dry air. This is not a safe operating mixture.

Hydrogen Lift Formula

The hydrogen lift calculator uses buoyancy based on the density difference between air and hydrogen.

F = V Δρ g
V = (F) / (Δρ g)

For an illustrative pure-hydrogen reference at 0°C and 101.325 kPa, the density difference is approximately:

Δρ = 1.202 kg / m³

All modes recompute density from temperature and absolute pressure. With hydrogen volume fraction f (remainder modeled as dry air):

Δρ = (fP(Mₐᵢᵣ - MH2)) / (RT)
  • F = hydrogen lift force, in newtons
  • V = hydrogen volume, in cubic meters
  • Δρ = density difference between air and hydrogen, in kg/m³
  • g = standard gravity, 9.80665 m/s²
  • P = air pressure, in pascals
  • T = air temperature, in kelvin
  • Mair = molar mass of dry air, 0.0289647 kg/mol
  • MH2 = molar mass of hydrogen, 0.00201588 kg/mol
  • R = ideal gas constant, 8.314462618 J/(mol·K)

Choose lift/payload, volume for payload, or comparison with pure helium. Gas-adjusted lift is F = VΔρg. Net payload mass is VΔρ minus envelope/rigging mass, and minimum volume is (payload + envelope mass)/Δρ. The model uses equal gas/ambient temperature and pressure. Defaults are 15°C,101.325 kPa and 100% hydrogen. Pure helium comparison uses the same volume and conditions; hydrogen purity applies only to the hydrogen mixture.

Typical Hydrogen Lift Values

These approximate reference values use pure hydrogen at 0°C and 101.325 kPa, with rounded Δρ = 1.202 kg/m³ and no envelope mass. The calculator recomputes full ideal-gas densities and may differ slightly from this rounded table.

Hydrogen volume Lift force Mass equivalent Approx. lbf
1 liter 0.01179 N 1.202 g 0.00265 lbf
1 ft³ 0.3338 N 34.0 g 0.0750 lbf
1 m³ 11.79 N 1.202 kg 2.65 lbf
10 m³ 117.88 N 12.02 kg 26.5 lbf
Air condition Approx. Δρ Lift per 1 m³
0°C, 101.325 kPa 1.202 kg/m³ 11.79 N
15°C, 101.325 kPa 1.140 kg/m³ 11.18 N
25°C, 101.325 kPa 1.102 kg/m³ 10.80 N
15°C, 90 kPa 1.012 kg/m³ 9.93 N

Hydrogen Lift Examples

Example 1: Find lift from hydrogen volume

You have 10 m³ of pure hydrogen at 0°C and 101.325 kPa, with zero envelope mass.

F ≈ 10 × 1.202322505 × 9.80665
F ≈ 117.91 N

The lift is about 117.91 N, equal to about 26.5 lbf or 12.02 kg mass equivalent.

Example 2: Find volume from required lift

For 50 N of gas-adjusted lift at 25°C and 101.325 kPa, use pure hydrogen and zero envelope mass. Enter payload mass 50/9.80665 kg (approximately 5.09858 kg); Δρ is approximately 1.101507269 kg/m³.

V ≈ (50) / (1.101507269 × 9.80665)
V ≈ 4.63 m³

You need about 4.63 m³ of hydrogen.

Hydrogen Lift FAQ

Is hydrogen lift the same as payload capacity?

No. The result is the buoyant lift from the hydrogen volume after accounting for the weight of the hydrogen gas itself. To estimate payload capacity, subtract the mass or weight of the balloon envelope, frame, lines, fittings, and any required safety margin.

Why does changing temperature or pressure change lift?

All modes recompute dry-air and gas densities. At fixed gas volume and equal gas/ambient conditions, warmer temperature or lower absolute pressure reduces the density difference and gas-adjusted lift. Real envelope expansion, gas temperature differences and humidity are not modeled.

Does humidity affect hydrogen lift?

Yes, humidity can slightly change air density. This calculator uses dry air in its ideal-gas density model. For most rough estimates, temperature and pressure have a larger effect than humidity.