Ideal Gas Law Calculator
Solve the ideal gas equation \(PV=nRT\) for pressure, volume, or temperature using your known gas conditions.
Calculation Steps
Practical Guide
Ideal Gas Law Calculator
This guide shows how to use the Ideal Gas Law Calculator correctly, interpret the outputs, and spot the common pitfalls. You’ll see when \(PV=nRT\) is valid, how to pick the right inputs and units, and how to sanity-check results with worked examples. The goal is simple: get reliable pressure, volume, or temperature estimates without forcing you to re-derive thermodynamics every time.
Quick Start
The calculator is based on the Ideal Gas Law: \[ PV = nRT \] where \(P\) is absolute pressure, \(V\) is volume, \(n\) is amount of gas (moles), \(R\) is the universal gas constant, and \(T\) is absolute temperature. Here’s the fastest safe workflow.
- 1 Choose what you want to compute in Solve For: Pressure \(P\), Volume \(V\), or Temperature \(T\). The calculator will hide that row automatically.
- 2 Enter the known variables. Use realistic engineering magnitudes (avoid “placeholder” zeros).
- 3 Confirm that your pressure input is absolute, not gauge. If you measured gauge pressure, convert it first: \[ P_{\text{abs}} = P_{\text{gauge}} + P_{\text{atm}} \] with \(P_{\text{atm}} \approx 101.325\ \text{kPa} = 14.7\ \text{psi}\).
- 4 Make sure temperature is in an absolute scale. If you input °C or °F, the calculator converts internally to K or °R: \[ T(K)=T(^{\circ}C)+273.15,\quad T(^{\circ}R)=T(^{\circ}F)+459.67 \]
- 5 Pick result units under Result Units (kPa, psi, m³, L, °C, K, etc.) to match your application.
- 6 Review Quick Stats and the equation banner. If \(PV\) and \(nRT\) don’t agree within rounding, you likely have a unit or absolute/gauge mistake.
- 7 Use Show Steps to verify the rearrangement and substituted values before you stamp a calculation into a report.
Tip: If your gas is near atmospheric pressure and room temperature, the ideal gas law is usually accurate to within a few percent for many common gases.
Watch out: At very high pressures, very low temperatures, or near condensation, real-gas effects can make \(PV=nRT\) underestimate or overestimate the true state.
Choosing Your Method
Engineers use the ideal gas law in a few recurring ways. The calculator supports the direct \(PV=nRT\) form, but you should pick the framing that best matches what you actually measured.
Method A — Direct \(PV=nRT\) with moles
Use this when the amount of gas is naturally expressed in moles (lab work, chemical processes, reaction stoichiometry).
- Matches the universal constant \(R=8.314462618\ \text{J/(mol·K)}\).
- Cleanest algebra; easy to rearrange for any variable.
- Ideal for mixtures when total moles are known.
- Field measurements are often mass-based, not mole-based.
- Requires a molar mass conversion if you start from kilograms or pounds.
Method B — Specific gas constant form \(PV=mR_sT\)
Best when you know the gas mass \(m\) instead of moles. Convert first, then still use the calculator.
- Natural for HVAC, compressed air systems, and engine cylinders.
- Mass is easy to measure or infer from flow meters.
- Requires gas identity and molar mass \(M\).
- You must convert to moles using \(n=m/M\).
Method C — Real-gas correction with compressibility \(Z\)
Use this when pressures are high or temperatures approach saturation. The calculator is still useful as a baseline.
- Captures real behavior in tanks, pipelines, and cryogenic work.
- Reduces systematic error versus ideal assumptions.
- Requires charts or EOS software to find \(Z\).
- More work than ideal gas; often overkill below ~5–10 bar.
In practice, apply Method A/B for everyday engineering sizing and sanity checks, and step up to Method C only when the ideal assumption is a known risk to safety or performance.
What Moves the Number the Most
Because the ideal gas law is multiplicative, a small mistake in any dominant variable scales right into your result. These are the main “levers” that swing the output:
Temperature must be absolute. Forgetting the \(+273.15\) or \(+459.67\) shift is the #1 source of huge errors. Pressure and volume are directly proportional to \(T\).
\(P\) in \(PV=nRT\) is absolute. A 50 psi gauge reading is ~64.7 psia. Missing this offset makes your computed volumes or temperatures too low.
If \(n\) comes from mass, convert with molar mass \(M\): \[ n=\frac{m}{M} \] A wrong molar mass (air vs nitrogen vs CO₂) gives a proportional error.
For tanks and vessels, volume uncertainty can dominate. Verify internal free volume (subtract liners, piping dead-legs, or liquid fill).
The calculator converts for you, but mixed assumptions still happen: e.g., using liters with psi without selecting correct units, or entering ft³ but thinking in gallons.
Near critical points, high pressures, or very low temperatures, \(Z\neq1\). The ideal calculation becomes a first guess that you should correct.
Worked Examples
These examples mirror typical use cases. Follow the same steps in the calculator to validate your own numbers.
Example 1 — Find Pressure in a Sealed Cylinder
- Known volume: \(V = 0.050\ \text{m}^3\) (50 L tank)
- Known amount: \(n = 2.00\ \text{mol}\)
- Known temperature: \(T = 35^{\circ}\text{C}\)
- Solve for: Pressure \(P\)
Interpretation: This is basically atmospheric pressure, which makes sense: 2 mol in a 50 L vessel at warm room temperature isn’t highly compressed.
Example 2 — Find Required Volume for Compressed Air
- Known pressure (absolute): \(P = 600\ \text{kPa}\) (≈ 5.9 atm)
- Known amount: \(n = 10.0\ \text{mol}\)
- Known temperature: \(T = 20^{\circ}\text{C}\)
- Solve for: Volume \(V\)
Interpretation: A ~41 L vessel at 600 kPa abs holds 10 mol of ideal gas at 20°C. If this were an air receiver, you would check whether real-gas effects are small at ~6 atm (they usually are for air).
Common Layouts & Variations
The same equation shows up across many disciplines. The table below summarizes common configurations and the extra checks you should do before trusting a pure ideal-gas result.
| Configuration / Use Case | Typical Known Inputs | Why Ideal Gas Works (or Doesn’t) | Practical Notes |
|---|---|---|---|
| Laboratory flask or syringe | \(n, V, T\) | Low pressure, far from saturation → \(Z\approx1\) | Use absolute temperature; small volumes make unit errors obvious. |
| Compressed air receiver | \(P, V, T\) → solve for \(n\) or \(m\) | Air is near-ideal below ~10 bar at ambient \(T\) | Confirm pressure is absolute; verify free internal volume. |
| Engine cylinder (intake/combustion) | \(P, V, T\) varying | Reasonable first-pass for intake states | During combustion, gases may deviate; use ideal as baseline only. |
| High-pressure gas bottle | \(P, n, T\) → solve for \(V\) | At high \(P\), real-gas effects matter | Apply \(Z\) correction if \(P\gtrsim 20\) bar or near critical \(T\). |
| Cryogenic or near-condensing gas | Any three variables | Often non-ideal; phase change risk | Do not rely on ideal gas law alone—check saturation curves/EOS. |
- Check that temperature is truly uniform (no hot spots or stratification).
- Use the gas identity you actually have, not “air” by default.
- Verify whether your pressure gauge reads absolute or gauge.
- For mixtures, total moles matter: \(n=\sum n_i\).
- If results look extreme, re-enter values in SI to validate units.
- Consider \(Z\) for high-pressure sizing or safety analysis.
Specs, Logistics & Sanity Checks
The ideal gas law is a model. It’s extremely useful, but only if you feed it defensible inputs. Before finalizing a design or troubleshooting a system, do these engineering checks.
Pressure sanity checks
- Convert gauge to absolute: add local atmospheric pressure.
- At altitude, \(P_{\text{atm}}\) is lower—don’t assume sea level.
- If computed \(P\) exceeds equipment rating, stop and reassess assumptions.
Volume sanity checks
- Use internal free volume (subtract liquid, liners, baffles, or dead-legs).
- For irregular vessels, validate volume geometrically or by water-fill tests.
- Be consistent: ft³, in³, L, and m³ differ by orders of magnitude.
Temperature sanity checks
- Measure where the gas is, not where the pipe wall is.
- Correct for transient heating/cooling if compression or expansion is rapid.
- Never input °C/°F thinking it is already absolute.
Rule of thumb: If your operating point is below ~5 bar and above ~0°C for common gases (air, N₂, O₂), the ideal model is typically fine for sizing and troubleshooting. If you’re near the limits of a pressure vessel, near saturation, or in cryogenic ranges, use the calculator as a first pass and then confirm with a real-gas method.