About the Ideal Gas Law Calculator
The Ideal Gas Law Calculator solves PV = nRT for whichever of the four variables you're missing, pressure, volume, moles, or temperature, given the other three. It's built for chemistry and physics problems where you know most of a gas sample's state and need the last piece, from a closed container's pressure buildup to how many moles of gas occupy a given flask.
How It Works
Choose which quantity to solve for, then enter the other three: pressure in atmospheres, volume in liters, amount in moles, and temperature in Kelvin. The tool rearranges PV = nRT algebraically using the gas constant R = 0.0820573 L atm/(mol K), then reports all four values with the one you solved for highlighted.
Formula & Methodology
To solve by hand, first convert temperature to Kelvin (add 273.15 to Celsius) since the law only holds on an absolute scale, then plug your three known values into the rearranged equation for the unknown. For example, solving for pressure with n = 1 mol, T = 273.15 K, and V = 22.4 L reproduces the classic result of 1 atm, the volume one mole of an ideal gas occupies at standard conditions. The gas constant used here, R = 0.0820573 L atm/(mol K), is scaled specifically for pressure in atmospheres and volume in liters; switching to SI units (pascals and cubic meters) instead requires R = 8.314 J/(mol K), so keeping units consistent matters as much as the algebra itself.
Examples
Standard conditions
With n = 1 mol, T = 273.15 K, and V = 22.4 L, solving for pressure gives P = (1 x 0.0820573 x 273.15) / 22.4, approximately 1.0004 atm, matching the familiar molar volume of a gas at STP.
Heated container
A rigid 10 L tank holding 2 mol of gas is heated to 350 K. Solving for pressure gives P = (2 x 0.0820573 x 350) / 10, approximately 5.744 atm.
Advantages
- Handles all four rearrangements of PV = nRT in one tool instead of requiring separate algebra for each variable.
- Uses atmosphere, liter, and Kelvin units consistently with the built-in R constant, removing a common source of unit-conversion mistakes.
- Flags impossible inputs, like zero volume, zero pressure, or zero Kelvin, with a clear message instead of returning NaN or Infinity.
Common Mistakes
- Entering temperature in Celsius or Fahrenheit instead of Kelvin, which throws off every calculation since the law depends on absolute temperature.
- Mixing units, entering pressure in kPa or volume in mL, without converting to atmospheres and liters first, which are what R = 0.0820573 assumes.
- Forgetting that this is an ideal gas approximation, and expecting exact results for gases under high pressure or near their condensation point.
Edge Cases to Watch For
- Solving for pressure or volume requires the denominator (volume or pressure respectively) to be nonzero, the calculator returns an error rather than dividing by zero.
- Solving for moles requires temperature above zero Kelvin, and solving for temperature requires moles above zero, since both appear as divisors.
- Real gases deviate from this law at high pressure or low temperature, where molecular volume and intermolecular attraction become significant, this calculator assumes ideal behavior throughout.
- Negative pressure, volume, or moles are not physically meaningful, but the calculator does not explicitly block them, so a stray negative entry passes through the arithmetic and produces a result without any real-world meaning.
Common Use Cases
- Chemistry students checking stoichiometry or gas law homework problems.
- Engineers estimating pressure buildup in a sealed vessel as temperature rises.
- Hobbyists working with compressed gas cylinders or scuba tanks who need a quick pressure or volume estimate.