What is the ideal gas law?

The ideal gas law is PV = nRT, where P is absolute pressure (Pa), V is volume (m³), n is the amount of gas in moles, R is the universal gas constant 8.314 462 618 J/(mol·K), and T is absolute temperature in Kelvin. It combines Boyle's law (P inversely proportional to V), Charles's law (V proportional to T) and Avogadro's law (V proportional to n) into one equation.

What value of R does this calculator use?

R = 8.314 462 618 J/(mol·K), the 2018 NIST CODATA recommended value. This is exact in the sense that it follows from the defined values of the Boltzmann constant k = 1.380 649 × 10⁻²³ J/K and the Avogadro constant N_A = 6.022 140 76 × 10²³ /mol, so R = k × N_A.

How do I convert between pressure units?

The calculator handles all conversions internally using exact factors: 1 atm = 101 325 Pa exactly; 1 bar = 100 000 Pa; 1 psi = 6 894.757 293 Pa; 1 mmHg = 1 torr = 133.322 387 Pa. Select your input unit and output unit independently — the tool converts to Pascals, solves, then converts back.

When does the ideal gas law break down?

The ideal gas approximation is excellent for most real gases at low-to-moderate pressures (below about 10 bar) and temperatures well above the boiling point of the gas. It breaks down at high pressures (intermolecular repulsion matters) and low temperatures (attraction between molecules matters). For those conditions use the van der Waals equation or an equation of state such as Peng-Robinson.

What is STP and what volume does 1 mole occupy?

IUPAC defines Standard Temperature and Pressure (STP) as 0 °C (273.15 K) and 100 kPa (1 bar, since 1982). At STP, 1 mole of an ideal gas occupies V = nRT/P = (1)(8.314)(273.15)/100 000 = 22.711 L. The older definition used 1 atm (101 325 Pa), giving the familiar 22.414 L/mol. This calculator lets you verify both by entering the respective conditions.

How do I find the number of moles from pressure, volume and temperature?

Select "Amount (mol)" as the solve-for variable, enter P, V and T in any units and the calculator returns n = PV / (RT). For example, 2 atm of gas in a 5 L flask at 25 °C gives n = (2 × 101 325)(0.005) / (8.314 × 298.15) = 0.408 mol.

Ideal Gas Law Calculator (PV = nRT)

The ideal gas law calculator solves PV = nRT for any one of the four state variables — pressure (P), volume (V), amount of substance (n) or temperature (T) — given the other three. It covers eight pressure units (Pa, kPa, MPa, bar, atm, psi, mmHg, torr), five volume units (m³, L, mL, cm³, ft³), three temperature scales (Kelvin, Celsius, Fahrenheit) and three molar units (mol, mmol, kmol), converting everything to SI internally before applying the formula and converting back to your preferred output unit.

The formula

The ideal gas law is:

PV = nRT

where each variable has a precise meaning:

P — absolute pressure, in Pascals (Pa) internally
V — volume, in cubic metres (m³) internally
n — amount of gas, in moles (mol)
T — absolute temperature, in Kelvin (K); subtract 273.15 from a Celsius reading to convert
R — the universal gas constant, 8.314 462 618 J/(mol·K) (2018 NIST CODATA value)

Rearranging gives four solving forms:

Solving for	Formula
Pressure	P = nRT / V
Volume	V = nRT / P
Moles	n = PV / (RT)
Temperature	T = PV / (nR)

The calculator uses whichever row matches your selection, with all inputs converted to SI before the arithmetic and the result converted back to your chosen display unit.

How it works

Every input passes through an exact unit-conversion factor to Pascals (or m³, mol, or K). The four rearrangements are then simple one-line divisions. The result is converted from SI to the output unit you select independently, so you can, for example, enter pressure in atm, volume in litres and temperature in Celsius, then read the mole count directly. The “Show working” panel displays all four SI values so you can verify the arithmetic step by step.

The gas constant used is R = k × N_A = 1.380 649 × 10⁻²³ × 6.022 140 76 × 10²³ = 8.314 462 618 J/(mol·K), which is the exact value implied by the 2019 SI redefinition.

Worked example

Problem: A sealed 5-litre flask contains 0.25 mol of nitrogen gas at 20 °C. What is the pressure in atm?

Step 1 — convert to SI:

V = 5 L = 0.005 m³
n = 0.25 mol
T = 20 °C = 293.15 K

Step 2 — apply P = nRT / V:

P = (0.25)(8.314 462 618)(293.15) / 0.005
P = (0.25 × 2438.0) / 0.005
P = 609.5 / 0.005
P = 121 900 Pa

Step 3 — convert to atm: 121 900 / 101 325 = 1.203 atm

So the flask holds approximately 1.2 atmospheres — slightly above standard atmospheric pressure, which is typical for a gas stored at room temperature.

Common reference points

Condition	P	V per mol
IUPAC STP (0 °C, 1 bar)	100 kPa	22.711 L
Old STP (0 °C, 1 atm)	101.325 kPa	22.414 L
Room temperature (25 °C, 1 atm)	101.325 kPa	24.465 L
Body temperature (37 °C, 1 atm)	101.325 kPa	25.447 L

All calculations run entirely in your browser — no data is ever uploaded or stored.