Ideal Gas Law PV
The Ideal Gas Law describes the thermodynamic state of an ideal gas, relating pressure ($P$), volume ($V$), moles ($n$), and absolute temperature ($T$).
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📐 Formula
💡 Practical Example
Solve for Volume (V) of 1.00 mole of gas at 1.00 atm pressure and 273.15 K (0°C): V = / 1.00 = 22.414 Liters (STP Standard Molar Volume).
📖 About Ideal Gas Law PV
The Ideal Gas Law describes the thermodynamic state of an ideal gas, relating pressure (P), volume (V), moles (n), and absolute temperature (T).
To use the Ideal Gas Law PV=nRT Chemistry Calculator, enter your Variable to Solve For, Pressure P (for V, n, T), Volume V (for P, n, T) and other values. The calculator instantly computes Calculated Target Variable Result, Gas Constant R Used and more. Results update in real time as you change any input — no submit button needed.
How to Use This Calculator
Enter your Variable to Solve For — choose from Pressure P (atm), Volume V (Liters), Moles n (mol), Pressure P (for V, n, T) (e.g. 1.00 in atm), Volume V (for P, n, T) (e.g. 22.414 in Liters (L)), Moles n (for P, V, T) (e.g. 1.00 in moles), and Temperature T (for P, V, n) (e.g. 273.15 in K (0°C)). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Ideal Gas Law: P × V = n × R × T
Pressure P = (n·R·T) ÷ V | Volume V = (n·R·T) ÷ P
Moles n = (P·V) ÷ (R·T) | Temperature T = (P·V) ÷ (n·R)
Where R = 0.082057 L·atm/(mol·K)
Worked Example
Solve for Volume (V) of 1.00 mole of gas at 1.00 atm pressure and 273.15 K (0°C):
V = / 1.00 = 22.414 Liters (STP Standard Molar Volume).
Understanding Your Result
US EPA fuel economy benchmarks (2024): Compact cars 28–35 MPG combined; midsize SUVs 22–28 MPG; pickup trucks 16–22 MPG; hybrid vehicles 40–55 MPG; EVs equivalent 90–120 MPGe. At 3.50/gallon, every 1 MPG improvement saves approximately 35–50/year over 10,000–15,000 annual miles. Real-world fuel economy typically runs 15–20% below EPA ratings in stop-and-go traffic, cold weather (reduces efficiency 15–25%), or with heavy loads.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.