Ideal Gas Law Calculator
Fast, accurate, and free online Ideal Gas Law Calculator tool that runs directly in your browser.
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Ideal gas calculator
R = 8.314462618 J/(mol K). For °C we convert to K. Make sure T>0 K.
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Other tools you may find usefulIdeal gas calculator PV = n·R·T - calculate P, V, n or T
The calculator uses the ideal gas equation of stateP·V = n·R·Tto determine one of four quantities:P(pressure),V(volume),n(number of moles) orT(temperature). The interface provides fields and unit selectorsP_unit= Pa, kPa, bar andT_unit= K, C. The unknown is selected bysolvewith a default value of "P". The result presentation is formatted withprecisionand displayed inout_value. The gas constant used has the valueR = 8.314462618 J·mol⁻¹·K⁻¹.
Description of fields and operating mode
- P– gas pressure. Units selected inP_unit: Pa, kPa, bar. Data is validated for reasonable process ranges.
- V– gas volume in cubic meters. Positive value and consistent with P and T.
- n– number of moles. It allows you to switch between macroscopic description and the amount of substance.
- T– temperature. Unit selected inT_unit: K or C. For °C, the calculator converts to kelvins.
- solve– selection of the unknown. Available: P, V, n, T.
- precision– number of decimal places in the result. Typically 2 to 4 ensures readability.
- out_value– calculation result according tosolve.
The calculator converts the units so that the equation is calculated in SI. If you specifyP_unit= kPa or bar, the values will be converted to Pa before substituting into PV = n·R·T.
Formulas and theory
Equation of state
PV = n · R · T
wherePis the pressure [Pa],Vis the volume [m³],nis the number of moles [mol],Tis the absolute temperature [K]. R is the universal gas constant 8.314462618 J·mol⁻¹·K⁻¹. The equation describes an ideal gas, i.e. a system with negligible intermolecular forces and zero self-volume of molecules. In practice, it is accurate for gases at low pressures and moderate temperatures.
Transformations for solve modes
solve = P
P = n · R · T / V
solve = V
V = n · R · T / P
solve = n
n = P · V / (R · T)
solve = T
T = P · V / (n · R)
Note the units of
- Pa is N m⁻². 1 kPa = 1000 Pa. 1 bar = 100 kPa = 100,000 Pa.
- ForT_unit= C the calculator uses T[K] = t[°C] + 273.15.
- Volume in SI is m³. If you are working in liters, convert V[L] to V[m³] according to 1 L = 1e−3 m³.
Model assumptions
- Ideal gas. The interactions between molecules are negligible.
- No condensation or chemical reactions.
- Homogeneous state in the controlled volume V.
Units and conversions in the interface
| Quantity | Symbol | Supported units | Default |
|---|---|---|---|
| Pressure | P | Pa, kPa, bar | Pa |
| Volume | V | m³ | m³ |
| Number of moles | n | mol | mol |
| Temperature | T | K, °C | K |
Examples of step-by-step calculations
Example 1 - determination of pressure P
- V = 0.012 m³
- n = 0.50 mol
- T = 300 K
P= n·R·T / V = 0.50 · 8.314462618 · 300 / 0.012 ≈ 103 930 Pa ≈ 104 kPa. You get a value close to atmospheric pressure.
Example 2 - determining the volume V
- P = 2 bar
- n = 0.20 mol
- T = 298 K
First, the pressure conversion. 2 bar = 200 kPa = 200,000 Pa.V= n·R·T / P = 0.20 · 8.314462618 · 298 / 200,000 ≈ 0.00248 m³ = 2.48 L.
Example 3 – determining the number of moles n
- P = 150 kPa
- V = 3.0 L = 0.003 m³
- T = 25 °C → 298.15 K
n= P·V / (R·T) = 150,000 · 0.003 / (8.314462618 · 298.15) ≈ 0.181 mol
Example 4 - determination of temperature T
- P = 101.325 kPa = 101 325 Pa
- V = 22.414 L = 0.022414 m³
- n = 1.0 mol
T= P·V / (n·R) = 101 325 · 0.022414 / 8.314462618 ≈ 273.15 K. We obtain the temperature of standard zero under STP conditions according to the classical definition of molar volume.
Engineering and teaching scenarios
| Scenario | Input data | Assumptions | Output |
|---|---|---|---|
| Gas cylinder | V, T, n | Ideal gas, no leaks | P and comparison to allowable |
| Weather balloon | P, T, n | Constant gas quantity | V and expansion rate |
| Sensor calibration | P, V, T | Known reference conditions | n to the nearest 1 percent |
| Laboratory calculations | P_unit, T_unit, V | Unit conversion | Selected solve with precision set in precision |
How to use the calculator
- Determine the unknown insolve. Choices: P, V, n, T.
- Fill in the known fields:P, V, n, T. ForPselect the unit inP_unit: Pa, kPa, bar.
- For temperature, setT_unit= K or C. In the case of °C, the calculator will automatically convert to K.
- Selectprecisionfor the desired result presentation.
- Run the calculations. The result will appear inout_valuewith a label corresponding tosolve.
Supporting materials
Typical reference conditions
- NTP 20 °C and 101.325 kPa.
- STP 0 °C and 101.325 kPa. The volume of 1 mole of an ideal gas is ≈ 22.414 L.
- Engineering: 25 °C and 100 kPa approximate laboratory conditions.
Quick conversions
- 1 bar = 100 kPa = 100,000 Pa.
- 1 L = 1e−3 m³.
- T[K] = t[°C] + 273.15.
PV = nRT - how to use the equation and what does pV/T = const
The ideal gas equationpV = nRT(Clapeyron equation) involves four quantities: pressure p [Pa], volume V [m³], number of moles n and temperature T [K]; R = 8.314 J/(mol·K) is the gas constant. The notation follows from the same equationpV/T = constfor a constant amount of gas - the basis of gas transformation problems:
| Transformation | Constants | Law | Dependence |
|---|---|---|---|
| Isothermal | T, n | Boyle-Mariotte | p₁V₁ = p₂V₂ |
| Isobaric | p, n | Gay-Lussac (volumetric) | V₁/T₁ = V₂/T₂ |
| Isochoric | V, n | Charles | p₁/T₁ = p₂/T₂ |
| Arbitrary (n = const) | n | joint equation | p₁V₁/T₁ = p₂V₂/T₂ |
Two traps that spoil the result most often: the temperaturemustbe in kelvins (T[K] = t[°C] + 273.15 - inserting degrees Celsius into pV = nRT is a classic mistake in tests) and the consistency of pressure units (1 atm = 101,325 Pa, 1 bar = 100,000 Pa, 1 hPa = 100 Pa). The calculator above takes care of both conversions automatically - just select which quantity you want to calculate, and enter the remaining three in any units from the list.
Common errors and pitfalls
- Mixing units. P in bar or kPa must be converted to Pa before substituting into PV = n·R·T.
- Temperature in °C in the equation. The equation requires kelvins. ForT_unit= C the calculator converts to K internally.
- Stress conditions. High pressures or very low temperatures cause deviations from the ideal gas. Real state equations are needed.
- Volume not in m³. Liters and milliliters without conversion will overestimate or underestimate the results by orders of magnitude.
- Heterogeneous mixture. The equation applies to one gas or mixture treated as ideal. For mixtures, use partial pressures and Dalton's law.
Extensions of calculations
Density and the ideal gas law
ρ = m/V = (n · M) / V = (P · M) / (R · T)
whereMis the molar mass. It allows you to quickly go from gas to density. Worth using when the goal is to evaluate balloon lift, mass flows, or ventilation selection.
Work in an isothermal process
W = n · R · T · ln(V2/V1)
Allows you to calculate the work of compression or expansion at constant temperature. Useful for verifying the energy requirements of compressors and vacuum processes.
Isobaric and isochoric process
- Isobaric: V ∝ T with constant P.
- Isochoric: P ∝ T with constant V.
These relationships allow for quick sanity checks when entering input data.
FAQ
Can I directly use °C instead of K
No. The equation requires absolute temperature in kelvins. In the interface, setT_unit= C, and the calculator will automatically convert to K before calculations.
What pressures are supported
InP_unityou select one of the options: Pa, kPa, bar. The calculator converts to Pa and validates typical laboratory and process ranges.
What if the result differs from the measurement
Probably the conditions do not meet the ideal gas assumptions or there are leaks. For high pressures and low temperatures, use the true state equation.
How to set the numerical presentation of the result
Theprecisionparameter controls the number of decimal places. A value of 3 is a good balance between readability and accuracy.
Does the calculator support gas mixtures
Yes, if you treat the mixture as an ideal one and apply Dalton's law to partial pressures. Otherwise, consider advanced models.
Summary
The ideal gas calculator allows you to quickly determine the pressure, volume, temperature or number of moles based on PV = n·R·T. Support for Pa, kPa, bar, K and °C units simplifies data entry. Thesolveparameter indicates an unknown, andprecisionformats the resultout_value. The tool is useful in teaching, laboratories and industrial processes, and the auxiliary sections extend the application to density and simple thermal processes. For extreme conditions and real gases, remember the limitations of the ideal model and the need to use more complex equations of state.