Temperature Calculator (Combined Gas Law)
Find the final temperature (T2) or initial temperature (T1) of a gas after its pressure and volume change.
Calculate Unknown Initial (T₁) or Final (T₂) Absolute Temperature: (P₁ · V₁) / T₁ = (P₂ · V₂) / T₂
Step-by-Step Mathematical Derivation:
1. Formula: T₂ = (P₂ × V₂ × T₁) / (P₁ × V₁)
2. Absolute Temperature Conversion:
• T₁ = 25 °C + 273.15 = 298.15 K
3. Substitution: (2.0 atm × 1.5 L × 298.15 K) / (1.0 atm × 2.0 L) = 447.23 K
4. Final Output: T₂ = 174.08 °C
This temperature calculator finds the final temperature (T2) of a gas after its pressure and volume change. Enter the initial pressure, initial volume, initial temperature, final pressure, and final volume, and the tool solves T2 = (P2 × V2 × T1) / (P1 × V1) with full steps. It also solves for initial temperature (T1) if you know the final state. It accepts K, °C, and °F, returns the answer in all three scales, supports atm, kPa, mmHg, torr, bar, and psi for pressure, and shows the substituted equation so you can check your work.
Quick Reference
| Item | Value |
|---|---|
| Formula for final temperature | T2 = (P2 × V2 × T1) / (P1 × V1) |
| Based on | Combined gas law, P1V1/T1 = P2V2/T2 |
| Solves for | T2 (final temperature) or T1 (initial temperature) |
| Temperature scale used in the formula | Kelvin (K = °C + 273.15) |
| Amount of gas | Must stay constant |
| Pressure type | Absolute pressure, not gauge pressure |
What Is Temperature in the Combined Gas Law?
Temperature measures the average kinetic energy of the particles in a gas. According to the kinetic molecular theory, hotter gas particles move faster, so they collide with container walls harder and more often. That is why temperature is tied to both pressure and volume.
The combined gas law links temperature to pressure and volume for a fixed amount of gas:
The law requires absolute temperature, measured on the Kelvin scale. The Kelvin scale is named after Lord Kelvin (William Thomson) and starts at absolute zero (0 K), the point of minimum particle motion. It merges Boyle's law, Charles's law, and Gay-Lussac's law, and it follows from the ideal gas law.
What This Temperature Calculator Finds
Use this tool when a gas changes pressure and volume and you need its new temperature. Typical cases include air compressed in a cylinder, a gas expanding into a larger container, or a sealed sample that must reach a target pressure and volume. Because the combined gas law depends only on the initial and final states, the answer holds no matter how the change happened.
Combined Gas Law Formula for Temperature
Start with the combined gas law:
Multiply both sides by T2 and by T1, then divide by P1V1 to isolate final temperature:
To find the initial temperature instead:
Variable Table
| Variable | Meaning | Common Units |
|---|---|---|
| P1 | Initial pressure | atm, kPa, mmHg, torr, bar, psi |
| V1 | Initial volume | L, mL, m³ |
| T1 | Initial absolute temperature | K |
| P2 | Final pressure | Same unit as P1 |
| V2 | Final volume | Same unit as V1 |
| T2 | Final absolute temperature (unknown) | K |
How to Use This Temperature Calculator
Choose the unknown
Select final temperature (T2) or initial temperature (T1).
Enter the temperature you know
Type in T1 (or T2) and pick K, °C, or °F. The tool converts it to Kelvin.
Enter both pressures
Fill in P1 and P2 and choose atm, kPa, mmHg, or another unit. Use the same unit for both.
Enter both volumes
Fill in V1 and V2 and choose L, mL, or m³. Use the same unit for both.
Click Calculate
The calculator applies the rearranged formula and returns the missing temperature in K, °C, and °F.
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 Pressure and Volume Affect Temperature" section.
What Can This Calculator Calculate?
Final temperature (T2)
The temperature of a gas after pressure and volume change together.
Initial temperature (T1)
The starting temperature when you know the final state.
To solve for a different unknown, use the dedicated pages: the Pressure Calculator for final pressure, the Volume Calculator for final volume, or the Combined Gas Law Calculator for all three unknowns in one tool.
Temperature Rearranged Formulas
All forms come from cross-multiplying P1V1/T1 = P2V2/T2 to get P1 × V1 × T2 = P2 × V2 × T1.
| Solve For | Formula |
|---|---|
| Final temperature | T2 = (P2 × V2 × T1) / (P1 × V1) |
| Initial temperature | T1 = (P1 × V1 × T2) / (P2 × V2) |
Read the T2 formula as a set of ratios:
The pressure ratio P2/P1 shows the Gay-Lussac's law effect, and the volume ratio V2/V1 shows the Charles's law effect. Multiply the starting temperature by both ratios to get the new temperature. This form is fast for mental estimates. Notice that the temperature ratio equals the ratio of the pressure-volume products: T2/T1 = (P2V2) / (P1V1).
Temperature Calculation Examples
Compression With a Pressure Rise
Problem: A gas is at 1.00 atm, 4.0 L, and 300 K. It is compressed to 3.0 L and its pressure rises to 2.00 atm. Find the final temperature.
Using the ratio form: 300 × (2.00 / 1.00) × (3.0 / 4.0) = 300 × 2 × 0.75 = 450 K. The pressure doubled while the volume shrank by only a quarter, so the gas heated up.
Celsius Input
Problem: A gas sample is at 101.3 kPa, 2.50 L, and 20 °C. It changes to 150 kPa and 2.00 L. Find the final temperature.
Syringe Compression
Problem: A syringe traps 50.0 mL of air at 1.00 atm and 25 °C. The plunger is pushed until the volume is 20.0 mL and the pressure is 3.00 atm. Find the final temperature.
The volume fell to 40% of the original, but pressure tripled instead of rising 2.5 times, so the temperature ends up higher. The mL unit cancels because both volumes use the same unit. In a real syringe, heat escapes into the surroundings quickly, so the actual temperature rise would be smaller than this ideal calculation predicts.
Mixed Units (mmHg, mL, L, °F Output)
Problem: A gas occupies 600 mL at 750 mmHg and 68 °F. It moves to a 0.50 L container at 1.00 atm. Find the final temperature.
The gas ends up colder because the pressure-volume product fell from 450,000 to 380,000 mmHg·mL.
Solve for Initial Temperature (T1)
Problem: A gas ends at 4.0 atm, 3.0 L, and 480 K. It started at 2.0 atm and 5.0 L. What was the initial temperature?
Temperature Conversion: Kelvin, Celsius, and Fahrenheit
The combined gas law needs Kelvin, so any Celsius or Fahrenheit value must be converted before you calculate. The calculator does this for you, and the formulas below let you check by hand.
| Conversion | Formula |
|---|---|
| Celsius to Kelvin | K = °C + 273.15 |
| Kelvin to Celsius | °C = K − 273.15 |
| Fahrenheit to Kelvin | K = (°F − 32) × 5/9 + 273.15 |
| Kelvin to Fahrenheit | °F = (K − 273.15) × 9/5 + 32 |
| Celsius to Fahrenheit | °F = °C × 9/5 + 32 |
| Fahrenheit to Celsius | °C = (°F − 32) × 5/9 |
Reference Temperature Benchmarks
| Description | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Absolute zero | −273.15 °C | −459.67 °F | 0 K |
| Water freezes | 0 °C | 32 °F | 273.15 K |
| Room temperature | 20 °C | 68 °F | 293.15 K |
| Common lab reference | 25 °C | 77 °F | 298.15 K |
| Human body | 37 °C | 98.6 °F | 310.15 K |
| Water boils (1 atm) | 100 °C | 212 °F | 373.15 K |
Why the Kelvin Scale Is Required
Gas pressure and volume are proportional to absolute temperature. Celsius and Fahrenheit have arbitrary zero points, so their ratios do not reflect real changes in particle energy. For example, heating a gas from 10 °C to 20 °C looks like a doubling in Celsius, but in Kelvin the change is from 283.15 K to 293.15 K, only about 3.5%. Using Celsius in the formula also risks division by zero at 0 °C and negative volumes or pressures below it.
Pressure and Volume Units
The combined gas law is a ratio, so any pressure unit and any volume unit work as long as the initial and final states use the same ones.
Pressure Units
| Pressure Unit | Equivalent |
|---|---|
| 1 atm | 101.325 kPa |
| 1 atm | 760 mmHg |
| 1 atm | 760 torr |
| 1 atm | 1.01325 bar |
| 1 atm | 14.696 psi |
Volume Units
| Volume Unit | Equivalent |
|---|---|
| 1 L | 1000 mL |
| 1 mL | 1 cm³ |
| 1 m³ | 1000 L |
How Pressure and Volume Affect Temperature
Use this table for a quick sense check of any result.
| Change | Effect on Temperature | Reason |
|---|---|---|
| Pressure increases, volume constant | Temperature increases | Gay-Lussac's law |
| Pressure decreases, volume constant | Temperature decreases | Gay-Lussac's law |
| Volume increases, pressure constant | Temperature increases | Charles's law |
| Volume decreases, pressure constant | Temperature decreases | Charles's law |
| Pressure increases and volume increases | Temperature increases strongly | Both effects push temperature up |
| Pressure decreases and volume decreases | Temperature decreases strongly | Both effects push temperature down |
| Pressure increases and volume decreases | Depends on the ratios | Compare P2/P1 with V1/V2 |
Real-World Examples of Gas Temperature Changes
Diesel engines
Air is compressed to a small fraction of its volume, and the resulting temperature rise ignites the fuel without a spark plug.
Bicycle pumps
The pump barrel warms up as air is compressed.
Fire pistons
A rapid compression stroke heats trapped air enough to ignite tinder.
Refrigerators and air conditioners
Refrigerant gas heats up when compressed and cools when it expands.
Aerosol cans
A can feels cold when sprayed because the gas expands as it leaves.
Scuba tanks
A tank warms while it is being filled and cools when air is released.
Weather and altitude
Rising air expands and cools as pressure drops.
When Can You Use This Temperature Calculator?
Use the combined gas law to find temperature 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 pressure and volume changes
You know P1, P2, V1, and V2.
Absolute units
Pressure is absolute, and the calculation is done in Kelvin.
Temperature Calculator vs Other Gas Law Tools
| Tool | Use It When | Formula |
|---|---|---|
| Temperature Calculator (this page) | Pressure and volume both change, and you need temperature | T2 = (P2 × V2 × T1) / (P1 × V1) |
| Charles's Law Calculator | Only volume changes, pressure constant | V1/T1 = V2/T2 |
| Gay-Lussac's Law Calculator | Only pressure changes, volume constant | P1/T1 = P2/T2 |
| Boyle's Law Calculator | Pressure and volume change, temperature constant | P1V1 = P2V2 |
| 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 temperature from moles, or the amount of gas changes | PV = nRT |
Common Temperature Calculation Mistakes
| Mistake | Why It Fails | Fix |
|---|---|---|
| Entering °C or °F in the formula | Gas laws need absolute temperature | Convert with K = °C + 273.15 |
| Forgetting to convert the answer back | The formula returns Kelvin | Convert with °C = K − 273.15 if needed |
| Using gauge pressure | Ignores atmospheric pressure | Add about 1 atm (14.7 psi) to get absolute |
| Mixing pressure units | atm and kPa in one ratio give a wrong answer | Convert P1 and P2 to one unit |
| Mixing volume units | mL and L in the same ratio break the result | Convert V1 and V2 to one unit |
| Swapping P1 and P2 | Inverts the pressure ratio and the answer | Use P2/P1 in the T2 formula |
| Swapping V1 and V2 | Inverts the volume ratio | Use V2/V1 in the T2 formula |
| Forgetting the constant amount rule | Moles must not change | Use the ideal gas law if gas is added or lost |
| Expecting a negative Kelvin result | Kelvin cannot be below 0 | Recheck inputs, since a negative result means a data error |
| Rounding too early | Small errors grow through the calculation | Keep extra digits and round at the end |
Temperature Calculator FAQs
Frequently asked questions about calculating gas temperature with the Combined Gas Law, Kelvin conversions, and heat.
How do you calculate final temperature with the combined gas law?
Use T2 = (P2 × V2 × T1) / (P1 × V1). Convert T1 to Kelvin, use matching units for both pressures and both volumes, substitute the values, and solve.
What is the formula for temperature in the combined gas law?
The formula is T2 = (P2 × V2 × T1) / (P1 × V1), which comes from rearranging P1V1/T1 = P2V2/T2.
Why must temperature be in Kelvin?
Gas pressure and volume are 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.
How do I convert Celsius to Kelvin?
Add 273.15 to the Celsius value. For example, 25 °C equals 298.15 K.
How do I convert Fahrenheit to Kelvin?
Subtract 32, multiply by 5/9, then add 273.15. For example, 68 °F equals 293.15 K.
Can this calculator convert temperature units on its own?
Yes. It accepts K, °C, and °F as input and returns the result in all three. The conversion table on this page also lets you check values by hand.
What happens to temperature if pressure and volume both increase?
Temperature rises strongly because both changes push it up. Higher pressure and larger volume together mean a larger PV product, and temperature is proportional to PV for a fixed amount of gas.
What if pressure increases and volume decreases?
Compare the products. If P2V2 is larger than P1V1, temperature rises. If it is smaller, temperature falls. If they are equal, temperature stays the same.
Can I solve for temperature 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.
Why do I get a negative temperature in kelvins?
Kelvin cannot go below 0, so a negative result signals an input error, such as gauge pressure entered instead of absolute pressure or swapped initial and final values.
Is the temperature 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.
Does the law tell me how much heat was added?
No. It relates the initial and final states only. Finding heat requires the gas's heat capacity and the type of process, which is beyond the combined gas law.