Productive ToolboxIdeal Gas Law Calculator
Calculate pressure, volume, moles, or temperature instantly using the Ideal Gas Law (PV = nRT). Supports multiple scientific units with real-time results.
Ideal Gas Law Calculator
Solve for any variable in PV = nRT. Select what to calculate, enter the three known values, and get the result instantly with full unit conversion.
Temperature (T)
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Solving for: Temperature (T)
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What is the Ideal Gas Law?
The Ideal Gas Law is a fundamental equation in chemistry and physics that describes the relationship between pressure, volume, temperature, and the amount of an ideal gas. The equation is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is absolute temperature.
The gas constant R equals 8.314472 J/(mol·K) in SI units. This law combines Boyle's Law (P ∝ 1/V at constant T), Charles's Law (V ∝ T at constant P), and Avogadro's Law (V ∝ n at constant P and T) into a single unified equation.
While real gases deviate from ideal behavior at very high pressures or very low temperatures, the Ideal Gas Law provides excellent approximations for most engineering and scientific calculations under standard conditions.
How to Use This Calculator
Step-by-Step Guide
- 1Select the variable you want to solve for (P, V, n, or T)
- 2Enter the three known values in their respective fields
- 3Select the appropriate unit for each input
- 4The result updates instantly as you type
- 5View the formula, substitution, and step-by-step breakdown
- 6Copy, save, or export the result as needed
Key Features
- ✓Solve for any of the four variables: P, V, n, or T
- ✓Real-time calculation as you type
- ✓6 pressure units: Pa, kPa, bar, atm, psi, mmHg
- ✓4 volume units: m³, L, mL, ft³
- ✓3 temperature units: K, °C, °F
- ✓Automatic SI unit conversion
- ✓Scientific notation for very large/small values
- ✓Formula visualization with substitution
- ✓Calculation history with localStorage
- ✓Export results as TXT file
- ✓Gas presets for common scenarios
Formula Variants
Solve for pressure when volume, moles, and temperature are known.
Solve for volume when pressure, moles, and temperature are known.
Solve for moles when pressure, volume, and temperature are known.
Solve for temperature when pressure, volume, and moles are known.
Example Calculations
| Solving For | Known Values | Result | Notes |
|---|---|---|---|
| Temperature (T) | P=2 atm, V=10 L, n=0.5 mol | T = 487.3 K | Above room temperature |
| Pressure (P) | V=5 L, n=2 mol, T=300 K | P = 9.84 atm | High pressure scenario |
| Volume (V) | P=1 atm, n=1 mol, T=273.15 K | V = 22.4 L | STP — molar volume |
| Moles (n) | P=101.325 kPa, V=1 L, T=298 K | n = 0.0409 mol | Room temperature, 1 L |
| Pressure (P) | V=22.4 L, n=1 mol, T=273.15 K | P = 1.000 atm | Validates STP |
| Temperature (T) | P=1 atm, V=11.2 L, n=0.5 mol | T = 273.15 K | Half molar volume at STP |
Unit Conversion Reference
Pressure Units
| Unit | Equivalent in Pa |
|---|---|
| 1 atm | 101,325 Pa |
| 1 bar | 100,000 Pa |
| 1 kPa | 1,000 Pa |
| 1 psi | 6,894.76 Pa |
| 1 mmHg | 133.322 Pa |
Temperature Conversions
Real-World Applications
Chemistry Labs
Calculate gas volumes, pressures, and moles in stoichiometry and reaction analysis.
Mechanical Eng.
Analyze compressed air systems, pneumatic actuators, and gas-powered machinery.
Thermodynamics
Model heat engines, refrigeration cycles, and thermodynamic processes.
Aerospace
Cabin pressurization, fuel systems, and atmospheric modeling at altitude.
Chemical Processing
Reactor design, gas storage tanks, and industrial process optimization.
Education
Core concept in chemistry, physics, and engineering courses worldwide.
Frequently Asked Questions
What is the Ideal Gas Law formula?
PV = nRT, where P is pressure (Pa), V is volume (m³), n is amount of substance (mol), R is the universal gas constant (8.314472 J/mol·K), and T is absolute temperature (K).
What is the value of the gas constant R?
R = 8.314472 J/(mol·K) in SI units. This is equivalent to 0.08206 L·atm/(mol·K) or 8.314 Pa·m³/(mol·K). This calculator uses the SI value and converts all inputs accordingly.
Why must temperature be in Kelvin?
The Ideal Gas Law requires absolute temperature. Kelvin starts at absolute zero (0 K = −273.15 °C), ensuring temperature is always positive. This calculator automatically converts Celsius and Fahrenheit to Kelvin before calculating.
What is Standard Temperature and Pressure (STP)?
STP is defined as 0 °C (273.15 K) and 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies exactly 22.414 liters — the molar volume. You can verify this using the calculator.
When does the Ideal Gas Law break down?
The Ideal Gas Law assumes no intermolecular forces and negligible molecular volume. It becomes less accurate at very high pressures (above ~10 atm), very low temperatures (near condensation), or for polar gases. For such cases, the van der Waals equation is more appropriate.
Can I use this for mixtures of gases?
Yes, using Dalton's Law of Partial Pressures. Each gas in a mixture behaves independently. Calculate each component separately using its partial pressure and mole count, then sum the results.
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