PV = nRT explained: the ideal gas law in plain terms
What each letter in PV = nRT means, why R has the value it does, and how to rearrange the formula to solve for any one variable.
What each symbol stands for
PV = nRT ties four properties of a gas together. P is pressure, the force the gas pushes on its container walls, here in atm or kPa. V is volume, the space the gas fills, in litres or cubic metres. The n is the amount of gas in moles, a count of particles where one mole is about 6.022 x 10^23 of them. T is the absolute temperature in kelvin, and R is the gas constant that makes the units balance. Read together, the equation says pressure times volume equals the amount of gas times its temperature, scaled by R.
Why R equals 0.082057
The gas constant R is not a free choice, it is fixed by the units around it. This tool works in atm, litres and kelvin, and in that system R is 0.082057 L atm per mol per kelvin. Switch to SI units of pascals, cubic metres and kelvin and the same constant becomes 8.314 J per mol per kelvin. Both describe the identical physics, they just carry different unit labels. That is why the calculator converts every input to atm, litres and kelvin first, applies the single value of R, then converts the answer back to whatever units you selected.
Rearranging to solve for one variable
Because the equation has four quantities, knowing any three pins down the fourth. Solve for pressure with P = nRT / V, for volume with V = nRT / P, for moles with n = PV / (RT), and for temperature with T = PV / (nR). The calculator does exactly this: the 'Solve for' menu removes one variable, you supply the other three, and it plugs them into the matching rearrangement. This is why molar volume at STP, one mole at 273.15 K and 1 atm, comes out as 22.41387 litres.
Where the ideal model breaks down
The ideal gas law assumes particles have no volume of their own and do not attract each other. That holds well for thin, warm gases like air at room conditions. Squeeze a gas to high pressure or chill it toward its boiling point and those assumptions fail: real molecules take up space and pull on their neighbours, so measured pressure and volume drift from the prediction. For those cases chemists reach for corrected equations such as van der Waals, but for homework, lab estimates and everyday gas problems the ideal law is accurate enough.