Ideal Gas Law (PV = nRT) Calculator
The ideal gas law PV = nRT ties pressure P, volume V, amount n and absolute temperature T into a single equation that underpins chemistry, physics and engineering. Pick any one unknown, type in the other three with their units, and the tool normalises everything to SI internally before solving — so you can freely mix atm with L, mol with °C, and so on.
Please enter valid numbers (pressure, volume and amount must be > 0; temperature must be above absolute zero).
Pressure
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Given
Volume
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Solved
Amount
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Temperature
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Formula
PV = nRT
Universal gas constant R = 8.314462618 J/(mol·K) (CODATA 2018). All math runs internally in SI units (Pa, m³, mol, K).
Formula
PV = nRT │ R = 8.314462618 J/(mol·K) (CODATA 2018) │ T must be absolute (K); °C and °F are converted via T_K = °C + 273.15 and (°F − 32) × 5⁄9 + 273.15.
- · All arithmetic runs internally in SI base units (Pa, m³, mol, K); the unit selectors are just I/O converters and do not affect precision.
- · Exact unit conversions: 1 atm = 101 325 Pa (exact); 1 bar = 10⁵ Pa (exact); 1 mmHg = 133.322 387 415 Pa; 1 psi ≈ 6 894.757 293 168 Pa; 1 L = 10⁻³ m³.
- · STP (IUPAC since 1982): T = 273.15 K, P = 1 bar, giving a molar volume of ~22.711 L/mol; the older STP (P = 1 atm) gives 22.414 L/mol.
- · The ideal-gas approximation assumes point-like molecules with no attractive forces. Deviations are smallest at low pressure and high temperature; near condensation (high P, low T) switch to van der Waals or another real-gas equation.
- · Temperature inputs must be above absolute zero (0 K = −273.15 °C = −459.67 °F); values at or below it are rejected.
- · References: CODATA 2018 recommended values (NIST); IUPAC Compendium of Chemical Terminology ("Gold Book", 2nd ed.), entries for "ideal gas" and "STP".
Frequently asked
Which value of R should I use?
Internally the tool always uses R = 8.314 462 618 J/(mol·K) (CODATA 2018) — your inputs are converted to Pa, m³ and K before R is applied, so unit choice cannot affect the answer. For hand calculations, chemistry textbooks often pick R = 0.082 057 L·atm/(mol·K) (P in atm, V in L) or R = 62.363 6 L·mmHg/(mol·K). If you check the result by hand, remember R changes value whenever you change units.
Is the molar volume at STP 22.4 L or 22.7 L?
Both are correct — it depends on which definition of STP your course uses. The old (pre-1982 IUPAC, and many older textbooks) STP is T = 273.15 K and P = 1 atm = 101 325 Pa, giving 22.414 L per mole of ideal gas. After 1982 IUPAC redefined STP to P = 1 bar = 100 000 Pa, giving 22.711 L/mol. If a question says "at STP" without specifying the pressure, check which convention is in play. NTP (20 °C, 1 atm) is about 24.055 L/mol.
When does PV = nRT break down?
The ideal-gas assumption fails whenever molecular volume or intermolecular forces become significant. Practical rule of thumb: above ~10 atm, or near a gas's boiling point (e.g. water vapour, CO₂ or propane near room temperature), switch to van der Waals — (P + a·(n/V)²)(V − nb) = nRT — or a more accurate equation of state such as Redlich-Kwong or Peng-Robinson. To quantify the deviation use the compressibility factor Z = PV/(nRT): Z = 1 for an ideal gas, and how far Z drifts from 1 measures non-ideality.
Can I use this to apply the combined gas law?
Indirectly, yes. The combined gas law P₁V₁/T₁ = P₂V₂/T₂ assumes the amount of gas n is constant. Workflow: run the tool once in "Solve for n" mode with state 1 (P₁, V₁, T₁) to get n, then run it again with the same n and any two known quantities from state 2 to solve for the third. Always feed temperatures in kelvin — °C cannot be plugged directly into a ratio.
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