Calculate the mass of Hydrogen gas ($H_2$) based on volume, pressure, and temperature.
The internal volume of the storage tank or container.
Please enter a valid positive volume.
Gauge pressure of the gas (1 Bar ≈ 14.5 PSI). Standard tanks often use 350 or 700 bar.
Please enter a valid positive pressure.
Ambient temperature of the gas.
Please enter a valid temperature.
Correction factor for real gas behavior. Use 1.0 for Ideal Gas. At 700 bar, Z ≈ 1.45.
Z factor must be positive.
Total Hydrogen Weight
0.00kg
Weight in Pounds
0.00 lbs
Energy Content (LHV)
0.00 kWh
Gas Density
0.00 kg/m³
Formula Used: Mass = (P × V × M) / (Z × R × T)
Where P is pressure (Pa), V is volume (m³), M is molar mass (0.002016 kg/mol), Z is compressibility, R is gas constant (8.314), and T is temperature (K).
Pressure vs. Weight Analysis
Chart shows how hydrogen weight increases with pressure at the current volume and temperature.
Detailed Breakdown
Pressure (Bar)
Weight (kg)
Energy (kWh)
What is a Hydrogen Weight Calculator?
A hydrogen weight calculator is a specialized engineering tool designed to determine the mass of hydrogen gas ($H_2$) stored within a specific volume under defined pressure and temperature conditions. Unlike liquids, gases are highly compressible, meaning their weight (mass) varies significantly based on environmental factors.
This tool is essential for engineers, energy analysts, and logistics professionals working with hydrogen fuel cells, industrial gas storage, or green energy projects. It helps in estimating fuel capacity, calculating transport loads, and determining the energy potential of stored hydrogen.
Common misconceptions include assuming hydrogen has a fixed weight per liter like water. In reality, 100 liters of hydrogen at 1 bar weighs almost nothing, while 100 liters at 700 bar weighs roughly 4-5 kg depending on temperature.
Hydrogen Weight Formula and Mathematical Explanation
The core calculation relies on the Ideal Gas Law, often modified with a compressibility factor ($Z$) for high-pressure scenarios (Real Gas Law). The formula is derived as follows:
PV = ZnRT
To solve for Mass ($m$), we rearrange the equation:
m = (P × V × M) / (Z × R × T)
Variable
Meaning
Unit Used in Formula
Typical Range
P
Absolute Pressure
Pascals (Pa)
1 – 70,000,000 Pa (1-700 Bar)
V
Volume
Cubic Meters ($m^3$)
0.05 – 100 $m^3$
M
Molar Mass of $H_2$
kg/mol
Constant: ~0.002016
Z
Compressibility Factor
Dimensionless
1.0 (Low Pressure) to ~1.5 (High Pressure)
R
Universal Gas Constant
J/(mol·K)
Constant: 8.314
T
Temperature
Kelvin (K)
233K – 323K (-40°C to 50°C)
Practical Examples (Real-World Use Cases)
Example 1: Fuel Cell Vehicle (FCEV) Tank
A standard hydrogen car might have a tank volume of 125 Liters rated for 700 Bar pressure at 25°C.
Input Volume: 125 Liters
Input Pressure: 700 Bar
Temperature: 25°C
Z Factor: ~1.46 (Hydrogen is less compressible at high pressure)
Calculated Weight: ~5.0 kg of Hydrogen
Financial Interpretation: At a pump price of $15/kg, a full tank costs roughly $75 and provides a range of about 300-400 miles.
Example 2: Industrial Buffer Tank
A factory stores hydrogen for backup power in a 5,000 Liter tank at a moderate pressure of 50 Bar.
Input Volume: 5,000 Liters
Input Pressure: 50 Bar
Temperature: 20°C
Z Factor: ~1.03
Calculated Weight: ~405 kg of Hydrogen
Energy Potential: Since hydrogen has a Lower Heating Value (LHV) of ~33.3 kWh/kg, this tank holds approximately 13,486 kWh of thermal energy.
How to Use This Hydrogen Weight Calculator
Enter Volume: Input the water volume capacity of your tank in Liters.
Enter Pressure: Input the gauge pressure in Bar. Common values are 350 or 700 for vehicles, and 200 for industrial cylinders.
Set Temperature: Adjust the temperature to match ambient conditions. Gas density decreases as temperature rises.
Adjust Z-Factor (Optional): For pressures below 50 Bar, leave as 1.0. For 350 Bar, use ~1.2. For 700 Bar, use ~1.45 for higher accuracy.
Analyze Results: Review the total weight in kg and the energy content in kWh to plan your storage or usage requirements.
Key Factors That Affect Hydrogen Weight Results
Understanding the variables in the hydrogen weight calculator is crucial for accurate estimations.
1. Pressure (Direct Correlation)
Pressure is the primary driver of density. Doubling the pressure roughly doubles the mass of gas stored, although the "law of diminishing returns" applies at very high pressures due to the compressibility factor.
2. Temperature (Inverse Correlation)
As temperature rises, gas expands. In a fixed volume tank, this increases pressure, but if filling to a specific pressure limit, a hotter tank holds less mass than a cold one. This is why vehicle fueling stations chill hydrogen to -40°C during dispensing.
3. Compressibility Factor (Z)
Hydrogen behaves like an ideal gas at low pressures. However, at high pressures (above 200 bar), intermolecular forces cause it to resist compression more than predicted by the Ideal Gas Law. Ignoring Z at 700 bar can lead to overestimating capacity by 30-40%.
4. Tank Expansion
Physical tanks expand slightly under high pressure (elastic deformation) and temperature. While minor, this increases the effective volume ($V$) slightly, allowing for marginally more mass.
5. Gas Purity
Industrial hydrogen is often 99.999% pure. Impurities like moisture or nitrogen have higher molar masses, which would technically increase the weight of the gas mixture, though usually negligible for fuel grade hydrogen.
6. Measurement Units
Confusion between Bar, PSI, and MPa is a common source of error. Always ensure you are converting units correctly before calculating. 1 Bar = 100,000 Pascals.
Frequently Asked Questions (FAQ)
What is the weight of 1 kg of hydrogen?
This is a trick question! 1 kg of hydrogen weighs exactly 1 kg. However, it occupies a massive volume: about 11,000 liters at standard atmospheric pressure and temperature.
How much energy is in 1 kg of hydrogen?
Hydrogen has a very high specific energy density. 1 kg of hydrogen contains approximately 33.3 kWh of energy (Lower Heating Value) or roughly 39.4 kWh (Higher Heating Value).
Why do I need a Z-factor?
The Z-factor corrects the Ideal Gas Law for real-world behavior. Without it, calculations for high-pressure storage (like FCEVs) would be inaccurate because hydrogen molecules repel each other under extreme pressure.
Does temperature affect the cost of filling a tank?
Indirectly, yes. If a tank is hot, it reaches its pressure limit with less gas inside. You pay for the mass (kg) dispensed, but you might leave with a "full" pressure tank that actually contains less range (fewer kg) than on a cold day.
What is the density of hydrogen at STP?
At Standard Temperature and Pressure (0°C, 1 atm), hydrogen density is approximately 0.08988 kg/m³, making it the lightest element in the universe.
Can I use this for other gases?
The formula works for other gases if you change the Molar Mass ($M$). However, this specific tool is calibrated with the molar mass of Hydrogen ($H_2$).
Is liquid hydrogen calculated differently?
Yes. Liquid hydrogen ($LH_2$) requires cryogenic temperatures (-253°C) and has a density of about 71 kg/m³. This calculator is for gaseous hydrogen only.
How accurate is this calculator?
It provides a high-quality estimation. For scientific precision, one would use a full Equation of State (EOS) like NIST REFPROP, but for engineering and financial estimates, this modified Ideal Gas Law approach is standard.