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Last updated: June 4, 2026

Ideal Gas Law Calculator

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Ideal Gas Law Calculator — PV = nRT

Scope and assumptions: This calculator applies the ideal gas model PV = nRT for uniform, well-mixed gases at equilibrium. Use SI units: P in Pa, V in m³, n in mol, T in K, and R = 8.314462618 J/(mol·K). Assumes ideal behavior (low to moderate pressure, sufficiently high temperature), negligible interactions, and no phase change.

Variables and units

  • P: Pressure [Pa]
  • V: Volume [m³]
  • n: Amount of substance [mol]
  • T: Absolute temperature [K]
  • R: Universal gas constant [8.314462618 J/(mol·K)]

Governing equations

  • P = n R T / V
  • V = n R T / P
  • n = P V / (R T)
  • T = P V / (n R)

Dimensional check: [P]·[V] = (Pa)(m³) = J; [n R T] = (mol)(J/(mol·K))(K) = J. Dimensions balance.

How to use the calculator

  1. Select which variable to solve for (P, V, n, or T).
  2. Enter the other three quantities in SI units. Keep R as default unless you explicitly change units consistently.
  3. Calculate. If a required input is zero or missing (e.g., V = 0), the tool flags an error.

Worked example (sanity check)

Problem: 1 mol of gas at T = 273.15 K occupying V = 0.022414 m³. Find P.

Inputs: n = 1 mol; T = 273.15 K; V = 0.022414 m³; R = 8.314462618 J/(mol·K).

Compute: P = n R T / V = (1)(8.314462618)(273.15) / 0.022414 ≈ 101324.997 Pa.

Result: P ≈ 1.01325 × 10^5 Pa (≈ 1 atm). This matches the reference example and provides a quick validation.

Model validity and limits

  • Good regimes: low to moderate pressures (roughly P ≲ a few bar), temperatures well above condensation, monatomic or light diatomic gases behave closest to ideal.
  • Breakdown indicators: high pressure, low temperature near saturation, strong intermolecular forces (e.g., polar gases), or very high densities. Consider real-gas corrections (van der Waals, virial) in these cases.
  • Temperature must be absolute (K). Converting: T[K] = T[°C] + 273.15.
  • Avoid mixed units (e.g., P in atm with R in SI). If using P in atm and V in L, use R ≈ 0.082057 L·atm/(mol·K) and keep all terms consistent.

Common pitfalls

  • Using gauge pressure instead of absolute pressure. Use absolute P; add atmospheric pressure to gauge measurements if necessary.
  • Not converting mL ↔ L ↔ m³: 1 L = 1e-3 m³.
  • Rounding too early; carry full precision through the calculation, round at the end.
  • Zero or near-zero divisors: V → 0 for P, P → 0 for V, n → 0 for T; these are non-physical or undefined in this model.

Quick checks

  • Proportionalities: At fixed n and V, P ∝ T; doubling T doubles P. At fixed n and T, P ∝ 1/V; halving V doubles P.
  • Energy scale: P V should be on the order of n R T (units of joules).

References

  • CODATA 2018: R = 8.314462618 J/(mol·K).
  • Standard conditions: 1 atm ≈ 101325 Pa; STP molar volume ≈ 22.414 L for ideal gas at 273.15 K and 1 atm.

Note: Educational guidance only; not a substitute for professional engineering review or laboratory safety protocols.

Frequently Asked Questions

What units does this calculator use?

SI units: P in pascals (Pa), V in cubic meters (m³), n in moles (mol), T in kelvin (K), R = 8.314462618 J/(mol·K).

Can I use atm and liters instead of Pa and m³?

Yes, but you must switch to R ≈ 0.082057 L·atm/(mol·K) and keep all inputs in atm, L, K, and mol consistently.

Should I use absolute or gauge pressure?

Use absolute pressure; add atmospheric pressure (≈101325 Pa) to gauge readings to convert.

When does the ideal gas law break down?

At high pressure, low temperature near condensation, or for strongly interacting gases; use real-gas models there.

Do I need to convert Celsius to kelvin?

Yes. T[K] = T[°C] + 273.15; the ideal gas law requires absolute temperature.

Why does the calculator reject zero values like V = 0 or n = 0?

Those lead to division by zero or non-physical states in this model; inputs must be finite and physically meaningful.

How can I sanity-check results?

Verify proportionalities (P ∝ T at fixed V,n; P ∝ 1/V at fixed T,n) and confirm PV ≈ nRT with units of joules.

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