Pressure Calculator (Combined Gas Law)
Find the final pressure (P2) or initial pressure (P1) of a gas after its volume and temperature change.
Calculate Unknown Initial (P₁) or Final (P₂) Pressure: (P₁ · V₁) / T₁ = (P₂ · V₂) / T₂
Step-by-Step Mathematical Derivation:
1. Formula: P₂ = (P₁ × V₁ × T₂) / (V₂ × T₁)
2. Absolute Temperature Conversion:
• T₁ = 25 °C + 273.15 = 298.15 K
• T₂ = 75 °C + 273.15 = 348.15 K
3. Substitution: (1.0 atm × 5.0 L × 348.15 K) / (2.5 L × 298.15 K)
4. Final Calculated Pressure: P₂ = 2.3355 atm
This pressure calculator finds the final pressure (P2) of a gas after its volume and temperature change. Enter the initial pressure, initial volume, initial temperature, final volume, and final temperature, and the tool solves P2 = (P1 × V1 × T2) / (V2 × T1) with full steps. It also solves for initial pressure (P1) if you know the final state. It supports atm, kPa, Pa, bar, mmHg, torr, and psi, converts Celsius and Fahrenheit to Kelvin automatically, and shows the substituted equation so you can check your work.
Quick Reference
| Item | Value |
|---|---|
| Formula for final pressure | P2 = (P1 × V1 × T2) / (V2 × T1) |
| Based on | Combined gas law, P1V1/T1 = P2V2/T2 |
| Solves for | P2 (final pressure) or P1 (initial pressure) |
| Temperature scale required | Kelvin (K = °C + 273.15) |
| Amount of gas | Must stay constant |
| Pressure type | Absolute pressure, not gauge pressure |
What Is Pressure in the Combined Gas Law?
Pressure is the force that gas particles exert on a surface per unit of area. In a container, it comes from countless collisions between gas particles and the walls. The SI unit of pressure is the pascal (Pa), named after the French mathematician and physicist Blaise Pascal, where 1 Pa equals 1 newton per square meter. Chemistry courses more often use atmospheres (atm), kilopascals (kPa), and millimeters of mercury (mmHg). The mmHg unit traces back to Evangelista Torricelli, who built the first mercury barometer in 1643. The torr is named in his honor.
The combined gas law links pressure to volume and temperature for a fixed amount of gas: According to the kinetic molecular theory, pressure rises when particles are squeezed into a smaller volume (more collisions per second) or when temperature rises (harder and faster collisions). The combined gas law captures both effects at once. It merges Boyle's law, Charles's law, and Gay-Lussac's law, and it follows from the ideal gas law.
What This Pressure Calculator Finds
Use this tool when a gas changes volume and temperature and you need its new pressure. Typical cases include a gas compressed in a cylinder while it heats up, a sealed sample that expands as it cools, or a lab gas measured at room conditions and moved to different ones.
Combined Gas Law Formula for Pressure
Start with the combined gas law:
Multiply both sides by T2 and divide by V2 to isolate final pressure:
To find the initial pressure instead:
Variable Table
| Variable | Meaning | Common Units |
|---|---|---|
| P1 | Initial pressure | atm, kPa, Pa, bar, mmHg, torr, psi |
| V1 | Initial volume | L, mL, m³ |
| T1 | Initial absolute temperature | K |
| P2 | Final pressure (unknown) | Same unit as P1 |
| V2 | Final volume | Same unit as V1 |
| T2 | Final absolute temperature | K |
How to Use This Pressure Calculator
Choose the unknown
Select final pressure (P2) or initial pressure (P1).
Enter the pressure you know
Type in P1 (or P2) and pick its unit, such as atm, kPa, or mmHg.
Enter both volumes
Fill in V1 and V2 and choose L, mL, or m³. Use the same unit for both.
Enter both temperatures
Fill in T1 and T2 in K, °C, or °F. The tool converts them to Kelvin.
Click Calculate
The calculator applies the rearranged formula and returns the missing pressure.
Read the steps
Check the substituted equation to see how the answer was found.
Run a sense check
Compare the direction of the change with the table in the "How Volume and Temperature Affect Pressure" section.
What Can This Calculator Calculate?
Final pressure (P2)
The pressure of a gas after volume and temperature change together.
Initial pressure (P1)
The starting pressure when you know the final state.
To solve for a different unknown, use the dedicated pages: the Volume Calculator for final volume, the Temperature Calculator for temperature conversions, or the Combined Gas Law Calculator for all three unknowns in one tool.
Pressure Rearranged Formulas
All forms come from cross-multiplying P1V1/T1 = P2V2/T2 to get P1 × V1 × T2 = P2 × V2 × T1.
| Solve For | Formula |
|---|---|
| Final pressure | P2 = (P1 × V1 × T2) / (V2 × T1) |
| Initial pressure | P1 = (P2 × V2 × T1) / (V1 × T2) |
Read the P2 formula as a set of ratios:
The volume ratio V1/V2 shows the Boyle's law effect, and the temperature ratio T2/T1 shows the Gay-Lussac's law effect. Multiply the starting pressure by both ratios to get the new pressure. This form is fast for mental estimates.
Pressure Calculation Examples
Compression and Heating
Problem: A gas has a pressure of 1.00 atm, a volume of 6.0 L, and a temperature of 300 K. It is compressed to 2.0 L and heated to 450 K. Find the final pressure.
Using the ratio form: 1.00 × (6.0 / 2.0) × (450 / 300) = 1.00 × 3 × 1.5 = 4.5 atm.
Expansion and Cooling
Problem: A gas sample is at 200 kPa, 3.0 L, and 25 °C. It expands to 5.0 L and cools to 0 °C. Find the final pressure.
Pressure drops because the volume grows and the gas also cools. Both changes lower the pressure.
Tire Pressure (Gauge to Absolute)
Problem: A car tire reads 32 psi on a gauge at 20 °C. After driving, the air heats to 50 °C. Assume the tire volume stays constant. What does the gauge read now?
This example shows why tire pressure should be checked when the tires are cold. It also shows why gauge readings must be converted to absolute pressure before applying gas laws.
Mixed Units (mmHg, mL, L, °F)
Problem: A gas occupies 500 mL at 760 mmHg and 68 °F. It is moved to a 0.40 L container at 86 °F. Find the final pressure in mmHg.
The pressure unit carries through because P1 and P2 share the same unit. The volume unit must match on both sides before you solve.
Solve for Initial Pressure (P1)
Problem: A gas ends at 3.0 atm, 4.0 L, and 400 K. It started at 8.0 L and 320 K. What was the initial pressure?
Pressure Units and Conversions
The combined gas law is a ratio, so any pressure unit works as long as P1 and P2 use the same one. Convert first if a problem mixes units.
| Unit | Equivalent |
|---|---|
| 1 atm | 101.325 kPa |
| 1 atm | 101,325 Pa |
| 1 atm | 760 mmHg |
| 1 atm | 760 torr |
| 1 atm | 1.01325 bar |
| 1 atm | 14.696 psi |
| 1 bar | 100 kPa |
| 1 kPa | 7.5006 mmHg |
| 1 psi | 6.895 kPa |
| 1 MPa | 1000 kPa |
Absolute Pressure vs Gauge Pressure
Gas laws need absolute pressure, which is measured from a perfect vacuum. Many instruments, such as tire gauges, read gauge pressure, which is measured relative to the surrounding atmosphere.
At sea level, atmospheric pressure is about 1 atm, 101.325 kPa, or 14.7 psi. A gauge reading of 0 psi still means the gas is at about 14.7 psi absolute. Forgetting this conversion is one of the biggest sources of wrong answers in real-world pressure problems.
Volume: use the same unit for V1 and V2. 1 L = 1000 mL = 1 dm³, and 1 m³ = 1000 L.
Temperature: always Kelvin. Convert with K = °C + 273.15 or K = (°F − 32) × 5/9 + 273.15. For quick conversions, use the Temperature Calculator.
How Volume and Temperature Affect Pressure
Use this table for a quick sense check of any result.
| Change | Effect on Pressure | Reason |
|---|---|---|
| Volume decreases, temperature constant | Pressure increases | Particles hit the walls more often (Boyle's law) |
| Volume increases, temperature constant | Pressure decreases | Particles spread out over more space |
| Temperature increases, volume constant | Pressure increases | Particles hit harder and faster (Gay-Lussac's law) |
| Temperature decreases, volume constant | Pressure decreases | Particles hit softer and slower |
| Volume decreases and temperature increases | Pressure increases strongly | Both effects push pressure up |
| Volume increases and temperature decreases | Pressure decreases strongly | Both effects push pressure down |
| Volume increases and temperature increases | Depends on the ratios | Compare V1/V2 with T2/T1 |
Real-World Examples of Gas Pressure Changes
Car and bicycle tires
Air heats up while driving, and pressure rises with temperature.
Bicycle pumps
Pushing the piston reduces volume and raises pressure, and friction also warms the air.
Diesel engines
Air in the cylinder is compressed to a fraction of its volume, and both pressure and temperature climb sharply.
Weather balloons
Outside pressure falls with altitude, so the balloon expands as the air inside cools.
Aerosol cans
Heat raises the propellant pressure, which is why cans warn against fire and hot cars.
Scuba tanks
Tank pressure changes with the temperature of the water and air around the cylinder.
Pressure cookers
Sealed heating raises pressure and lets water reach temperatures above 100 °C.
When Can You Use This Pressure Calculator?
Use the combined gas law to find pressure when all of the following are true:
Constant amount of gas
The number of moles stays the same. No leaks, no added gas, no reactions.
Same gas sample
You track one sample from an initial state to a final state.
Known volume and temperature changes
You know V1, V2, T1, and T2.
Absolute units
Temperature is in Kelvin and pressure is absolute.
Pressure Calculator vs Other Gas Law Tools
| Tool | Use It When | Formula |
|---|---|---|
| Pressure Calculator (this page) | Volume and temperature both change, and you need pressure | P2 = (P1 × V1 × T2) / (V2 × T1) |
| Boyle's Law Calculator | Only volume changes, temperature constant | P1V1 = P2V2 |
| Gay-Lussac's Law Calculator | Only temperature changes, volume constant | P1/T1 = P2/T2 |
| Charles's Law Calculator | Volume and temperature change, pressure constant | V1/T1 = V2/T2 |
| Combined Gas Law Calculator | You want to solve for any of P, V, or T | P1V1/T1 = P2V2/T2 |
| Ideal Gas Law Calculator | You need pressure from moles, or the amount of gas changes | PV = nRT |
Common Pressure Calculation Mistakes
| Mistake | Why It Fails | Fix |
|---|---|---|
| Using °C or °F | Gas laws need absolute temperature | Convert with K = °C + 273.15 |
| Using gauge pressure | Ignores atmospheric pressure | Add about 1 atm (14.7 psi) to get absolute |
| Mixing pressure units | atm and kPa in one equation break the ratio | Convert P1 to one unit before solving |
| Mixing volume units | mL and L in one ratio give a wrong answer | Convert V1 and V2 to the same unit |
| Swapping V1 and V2 | Inverts the volume ratio and the answer | Use V1/V2, not V2/V1, in the P2 formula |
| Swapping T1 and T2 | Inverts the temperature ratio | Use T2/T1 in the P2 formula |
| Forgetting the constant amount rule | Moles must not change | Use the ideal gas law if gas is added or lost |
| Assuming a rigid container | Flexible containers change volume | Use the actual V2 or apply the correct single-variable law |
| Rounding too early | Small errors grow through the calculation | Keep extra digits and round at the end |
| Skipping the sense check | Wrong answers go unnoticed | Compare the result with the direction table above |
Pressure Calculator FAQs
Frequently asked questions about calculating gas pressure with the Combined Gas Law, unit conversions, and absolute vs gauge pressure.
How do you calculate final pressure with the combined gas law?
Use P2 = (P1 × V1 × T2) / (V2 × T1). Convert temperatures to Kelvin, use matching units for both volumes, substitute the values, and solve.
What is the formula for pressure in the combined gas law?
The formula is P2 = (P1 × V1 × T2) / (V2 × T1), which comes from rearranging P1V1/T1 = P2V2/T2.
Why must temperature be in Kelvin when calculating pressure?
Gas pressure is proportional to absolute temperature. Kelvin starts at absolute zero, so ratios such as T2/T1 reflect real changes in particle energy. Celsius and Fahrenheit give incorrect results.
Can I use any pressure unit?
Yes, as long as P1 and P2 use the same unit. Common choices are atm, kPa, Pa, bar, mmHg, torr, and psi. The calculator converts them for you.
What is the difference between absolute pressure and gauge pressure?
Absolute pressure is measured from a perfect vacuum. Gauge pressure is measured relative to atmospheric pressure. Absolute equals gauge plus atmospheric pressure, and gas laws need absolute pressure.
What happens to pressure if volume decreases and temperature increases?
Pressure rises sharply because both changes push in the same direction. A smaller volume causes more wall collisions, and a higher temperature makes each collision stronger.
What if volume and temperature change in opposite directions?
Compare the ratios. Pressure rises if V1/V2 is larger than T1/T2 and falls if it is smaller. The calculator handles this automatically.
Can I solve for pressure if the amount of gas changes?
No. The combined gas law requires a constant number of moles. Use the ideal gas law (PV = nRT) instead.
How do I convert atm to kPa or mmHg?
Multiply by 101.325 for kPa or by 760 for mmHg. For example, 2.0 atm equals 202.65 kPa or 1520 mmHg.
Is the pressure calculator accurate for real gases?
It is accurate at low to moderate pressure and temperatures well above the boiling point. At very high pressure or near condensation, real gases deviate from ideal behavior.
What is standard pressure?
IUPAC defines standard pressure as 100 kPa (1 bar). Many textbooks still use 1 atm, which is 101.325 kPa. Check which value your course uses.
How is this different from the Boyle's law calculator?
The Boyle's law calculator assumes temperature is constant. This pressure calculator handles cases where volume and temperature both change.