Ideal Gas Law Calculator (PV = nRT)
Solve pressure, volume, moles, or temperature with unit conversion, worked examples, and an instant gas-state visual.
What can you enter?
Enter three gas variables and leave exactly one blank. The calculator converts units into atm, liters, and Kelvin before using PV = nRT.
| Variable | Accepted input | Internal unit | Blank means |
|---|---|---|---|
| Pressure P | atm, kPa, or Pa | atm | Solve P = nRT / V |
| Volume V | L or mL | L | Solve V = nRT / P |
| Moles n | mol | mol | Solve n = PV / RT |
| Temperature T | K, C, or F | K | Solve T = PV / nR |
Formula used
Worked example: STP pressure
Input: V = 22.414 L, n = 1.000 mol, T = 273.15 K, and pressure left blank.
- Start with PV = nRT.
- Rearrange for pressure: P = nRT / V.
- Substitute values: P = (1.000 mol)(0.082057)(273.15 K) / 22.414 L.
- P = 1.000 atm, which matches the common STP benchmark for one mole of ideal gas.
Built-in example data
| Example | Given values | Blank | Why it is useful |
|---|---|---|---|
| STP benchmark | V = 22.414 L, n = 1 mol, T = 273.15 K | P | Checks the classic 1 atm result. |
| Lab gas sample | P = 98.6 kPa, V = 250 mL, T = 24 C | n | Practices mL to L and C to K conversion. |
| Balloon volume | P = 1 atm, n = 0.5 mol, T = 298.15 K | V | Shows volume scaling with gas amount. |
| Solve temperature | P = 1.2 atm, V = 10 L, n = 0.42 mol | T | Returns temperature in the selected unit. |
| Pressure in Pa | V = 5 L, n = 0.2 mol, T = 300 K | P | Practices atm to Pa output. |
Why this calculator keeps users on track
Gas law problems are often unit problems disguised as algebra. This page shows the selected unit, the converted internal value, the rearranged formula, and a gas-state visual so users can catch mistakes before copying an answer.
| Need | How the page helps |
|---|---|
| Homework checking | Shows the formula, converted values, and final unit. |
| Exam revision | Built-in examples cover solving P, V, n, and T. |
| Lab preparation | Handles mL, kPa, Pa, Celsius, and Fahrenheit conversions. |
| Concept review | The visual links pressure, volume, moles, and temperature. |
| Result confidence | The STP benchmark helps users sanity-check answers. |
Which gas law does PV = nRT include?
The ideal gas law combines several gas relationships into one equation. If n and T stay constant, PV = nRT behaves like Boyle's law. If P and n stay constant, volume changes with absolute temperature like Charles's law. If V and n stay constant, pressure changes with absolute temperature like Gay-Lussac's law.
For classroom work, PV = nRT is the most flexible form because it can solve pressure, volume, moles, or temperature in one setup.
Common mistakes to avoid
- Entering Celsius directly into PV = nRT instead of converting to Kelvin.
- Using mL with R = 0.082057 without converting volume to liters.
- Mixing kPa or Pa with an atm-based gas constant.
- Leaving more than one variable blank.
- Using the ideal gas model at high pressure, low temperature, or near condensation without noting real-gas behavior.
Rounding and result checking
Use a gas constant that matches the units in the calculation. This calculator uses R = 0.082057 L atm mol^-1 K^-1 internally, so it converts pressure, volume, and temperature first. A helpful check is the one-mole benchmark: at 273.15 K and 1 atm, an ideal gas occupies about 22.414 L. If your answer is far from that pattern, inspect the units before trusting the result.
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Ideal Gas Law Calculator (PV = nRT) FAQs
Can you use combined gas law with mL?
Yes, certainly. The combined gas law P1V1/T1 = P2V2/T2 works with any volume unit (mL, L, cm3, m3) as long as you use the same unit on both sides. The volume terms appear as a ratio, so the units cancel automatically. The only strict rule is that temperature must be in Kelvin, otherwise the equation collapses (T cannot be zero or negative, and 0 °C is not zero kelvin). For pressure, atm/mmHg/Pa all work — just be consistent. P1V1/T1 = P2V2/T2 (T in Kelvin)
What is the Ideal Gas Law?
The ideal-gas law combines Boyle's, Charles's, Gay-Lussac's and Avogadro's laws into one simple equation: PV = nRT. Here P is pressure, V is volume, n is moles, T is absolute temperature (K), and R is the universal gas constant. It assumes the gas molecules are point particles, undergo perfectly elastic collisions and have no intermolecular forces — true at low pressure and high temperature. Real gases deviate and need the more sophisticated van der Waals equation for accurate behaviour. P · V = n · R · T
What is R in the Ideal Gas Law?
R is the universal gas constant. Its value depends on the units chosen: R = 0.0821 L·atm·K-1·mol-1 (most common in chemistry); R = 8.314 J·K-1·mol-1 (in SI units, used in thermodynamics); R = 62.36 L·mmHg·K-1·mol-1. R is the same for all ideal gases — that is what makes it “universal”. Always pick the R value that matches the units of the other variables you are using to avoid headaches!
Which equation represents the combined gas law?
The combined gas law unites Boyle's, Charles's and Gay-Lussac's laws into one form. It states that the ratio P V/T for a fixed amount of gas remains constant. In comparing two states: P1V1/T1 = P2V2/T2. It is extremely useful when all three of P, V and T change simultaneously — a common situation in real gas problems. Always remember to convert °C to K (T(K) = t(°C) + 273). P1V1/T1 = P2V2/T2 = constant
Which equation agrees with the Ideal Gas Law?
Any equation derivable from PV = nRT agrees with it. So all of Boyle's law (PV = const at constant n, T), Charles's law (V/T = const at constant n, P), Gay-Lussac's law (P/T = const at constant n, V), Avogadro's law (V/n = const at constant T, P), and the combined gas law are special cases. They appear different but are all the ideal-gas law in disguise, with one or more variables held constant.
What is the constant in the Ideal Gas Law?
The constant in PV = nRT is R, the universal gas constant. R = 0.0821 L·atm·K-1·mol-1 = 8.314 J·K-1·mol-1. It is universal because any ideal gas at the same T and P with the same number of moles occupies the same volume — Avogadro's hypothesis. Numerically, 1 mol of an ideal gas at STP (0 °C, 1 atm) occupies 22.4 L. R is one of the fundamental constants of physical chemistry.
What are the 3 gas laws?
The three classical gas laws are: (1) Boyle's Law — at constant T and n, P ∝ 1/V (P1V1 = P2V2). (2) Charles's Law — at constant P and n, V ∝ T (V1/T1 = V2/T2). (3) Gay-Lussac's Law — at constant V and n, P ∝ T (P1/T1 = P2/T2). Together with Avogadro's law (V ∝ n at constant T, P), they combine into the ideal-gas law.
How to find T2 in combined gas law?
Rearrange the combined gas law to solve for the unknown: T2 = T1 × (P2V2) / (P1V1). Always plug T1 in Kelvin (add 273.15 to °C). Example: a gas at 300 K, 1 atm, 2 L is changed to 2 atm and 1 L. Then T2 = 300 × (2 × 1)/(1 × 2) = 300 K. The temperature has stayed the same, as PV is unchanged. T2 = T1 · (P2V2) / (P1V1)
How to find V2 in combined gas law?
Rearrange similarly: V2 = V1 × (P1/P2) × (T2/T1). So V2 increases when pressure drops or temperature rises, and decreases otherwise — exactly what intuition suggests. Example: 5 L of gas at 300 K, 1 atm is heated to 600 K and pressure raised to 2 atm. V2 = 5 × (1/2) × (600/300) = 5 × 0.5 × 2 = 5 L. The two effects cancel. V2 = V1 · (P1/P2) · (T2/T1)