Volume Calculator (Combined Gas Law)
Find the final volume (V2) or initial volume (V1) of a gas after its pressure and temperature change.
Calculate Unknown Initial (V₁) or Final (V₂) Gas Volume: (P₁ · V₁) / T₁ = (P₂ · V₂) / T₂
Step-by-Step Mathematical Derivation:
1. Formula: V₂ = (P₁ × V₁ × T₂) / (P₂ × T₁)
2. Absolute Temperature Conversion:
• T₁ = 20 °C + 273.15 = 293.15 K
• T₂ = 80 °C + 273.15 = 353.15 K
3. Substitution: (2.0 atm × 10.0 L × 353.15 K) / (4.0 atm × 293.15 K)
4. Final Calculated Volume: V₂ = 6.0234 L
This volume calculator finds the final volume (V2) of a gas after its pressure and temperature change. Enter the initial pressure, initial volume, initial temperature, final pressure, and final temperature, and the tool solves V2 = (P1 × V1 × T2) / (P2 × T1) with full steps. It also solves for initial volume (V1) if you know the final state. It supports L, mL, m³, cm³, and other volume units, accepts atm, kPa, mmHg, torr, bar, and psi for pressure, 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 volume | V2 = (P1 × V1 × T2) / (P2 × T1) |
| Based on | Combined gas law, P1V1/T1 = P2V2/T2 |
| Solves for | V2 (final volume) or V1 (initial volume) |
| Temperature scale required | Kelvin (K = °C + 273.15) |
| Amount of gas | Must stay constant |
| Pressure type | Absolute pressure, not gauge pressure |
What Is Volume in the Combined Gas Law?
The volume of a gas is the space it occupies. Unlike a solid or liquid, a gas expands to fill its container, so its volume depends on the container size, the pressure applied to it, and its temperature. The SI unit of volume is the cubic meter (m³), but chemistry usually uses liters (L) and milliliters (mL). One liter equals one cubic decimeter (dm³), and one milliliter equals one cubic centimeter (cm³).
The combined gas law links volume to pressure and temperature for a fixed amount of gas: According to the kinetic molecular theory, gas particles move freely and collide with the walls of their container. When pressure rises, the gas is squeezed into a smaller volume. When temperature rises, particles move faster and push outward, so the gas expands if the container is flexible. 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 Volume Calculator Finds
Use this tool when a gas changes pressure and temperature and you need its new volume. Typical cases include a weather balloon rising through the atmosphere, a gas sample collected in a lab at room conditions and converted to standard conditions, or air in a cylinder that is compressed and heated.
Combined Gas Law Formula for Volume
Start with the combined gas law:
Multiply both sides by T2 and divide by P2 to isolate final volume:
To find the initial volume 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 (unknown) | Same unit as V1 |
| T2 | Final absolute temperature | K |
How to Use This Volume Calculator
Choose the unknown
Select final volume (V2) or initial volume (V1).
Enter the volume you know
Type in V1 (or V2) and pick its unit, such as L, mL, or m³.
Enter both pressures
Fill in P1 and P2 and choose atm, kPa, mmHg, or another unit. 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 volume.
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 Temperature Affect Volume" section.
What Can This Calculator Calculate?
Final volume (V2)
The volume of a gas after pressure and temperature change together.
Initial volume (V1)
The starting volume when you know the final state.
To solve for a different unknown, use the dedicated pages: the Pressure Calculator for final pressure, the Temperature Calculator for temperature conversions, or the Combined Gas Law Calculator for all three unknowns in one tool.
Volume Rearranged Formulas
All forms come from cross-multiplying P1V1/T1 = P2V2/T2 to get P1 × V1 × T2 = P2 × V2 × T1.
| Solve For | Formula |
|---|---|
| Final volume | V2 = (P1 × V1 × T2) / (P2 × T1) |
| Initial volume | V1 = (P2 × V2 × T1) / (P1 × T2) |
Read the V2 formula as a set of ratios:
The pressure ratio P1/P2 shows the Boyle's law effect, and the temperature ratio T2/T1 shows the Charles's law effect. Multiply the starting volume by both ratios to get the new volume. This form is fast for mental estimates.
Volume Calculation Examples
Expansion and Cooling
Problem: A gas has a volume of 2.0 L at 1.00 atm and 300 K. The pressure drops to 0.50 atm and the temperature falls to 270 K. Find the final volume.
Using the ratio form: 2.0 × (1.00 / 0.50) × (270 / 300) = 2.0 × 2 × 0.9 = 3.6 L. Halving the pressure doubles the volume, and the small temperature drop trims it back a little.
Weather Balloon
Problem: A weather balloon holds 1000 L of helium at 101.3 kPa and 25 °C at ground level. At altitude, the pressure is 25.0 kPa and the temperature is −50 °C. Find the balloon volume at altitude.
The balloon triples in volume because the pressure drops to about a quarter of its ground value, while the cold air only partly offsets the expansion. This is why weather balloons are launched only partly inflated.
Correcting a Lab Gas Volume to STP
Problem: A gas sample collected in a lab occupies 250 mL at 740 mmHg and 22 °C. What volume would it occupy at 760 mmHg and 0 °C?
The mL and mmHg units carry through because both states use the same units. Only temperature needed conversion. This kind of correction is common in gas collection experiments.
Mixed Units (atm, kPa, °F)
Problem: A 3.0 L gas sample is at 2.0 atm and 68 °F. The pressure changes to 150 kPa and the temperature rises to 104 °F. Find the final volume.
Solve for Initial Volume (V1)
Problem: A gas ends at 5.0 L, 2.0 atm, and 400 K. It started at 1.0 atm and 300 K. What was the initial volume?
Volume Units and Conversions
The combined gas law is a ratio, so any volume unit works as long as V1 and V2 use the same one. Convert first if a problem mixes units.
| Unit | Equivalent |
|---|---|
| 1 L | 1000 mL |
| 1 L | 1 dm³ |
| 1 mL | 1 cm³ |
| 1 m³ | 1000 L |
| 1 m³ | 1,000,000 cm³ |
| 1 US gallon | 3.78541 L |
| 1 ft³ | 28.3168 L |
Pressure: use the same unit for P1 and P2. 1 atm = 101.325 kPa = 760 mmHg = 760 torr = 1.01325 bar = 14.696 psi. Use absolute pressure, not gauge pressure. Absolute pressure equals gauge pressure plus atmospheric pressure.
Temperature: always Kelvin. Convert with K = °C + 273.15 or K = (°F − 32) × 5/9 + 273.15. For quick conversions, use the Temperature Calculator.
Molar Volume Reference
The volume of one mole of an ideal gas depends on temperature and pressure. Use these values as a check.
| Condition | Temperature | Pressure | Molar Volume |
|---|---|---|---|
| Older STP (many textbooks) | 273.15 K | 1 atm (101.325 kPa) | 22.414 L/mol |
| IUPAC STP | 273.15 K | 100 kPa | 22.711 L/mol |
| Room conditions (common reference) | 298.15 K | 1 atm | 24.465 L/mol |
If you know the moles of gas, use the Ideal Gas Law Calculator to find volume directly.
How Pressure and Temperature Affect Volume
Use this table for a quick sense check of any result.
| Change | Effect on Volume | Reason |
|---|---|---|
| Pressure increases, temperature constant | Volume decreases | Gas is compressed (Boyle's law) |
| Pressure decreases, temperature constant | Volume increases | Gas expands into the lower pressure |
| Temperature increases, pressure constant | Volume increases | Faster particles push outward (Charles's law) |
| Temperature decreases, pressure constant | Volume decreases | Slower particles push less |
| Pressure decreases and temperature increases | Volume increases strongly | Both effects push volume up |
| Pressure increases and temperature decreases | Volume decreases strongly | Both effects push volume down |
| Pressure increases and temperature increases | Depends on the ratios | Compare T2/T1 with P2/P1 |
Real-World Examples of Gas Volume Changes
Weather balloons
Outside pressure falls with altitude, so the balloon expands even as the air cools.
Scuba diving
Air in the lungs and buoyancy devices shrinks as a diver descends and expands as the diver ascends.
Syringes and pumps
Pulling or pushing the plunger changes the volume and pressure of the trapped air.
Hot air balloons
Heating the air inside raises its volume, which lowers its density and creates lift.
Internal combustion engines
Gas in the cylinder is compressed and then expands as it burns and heats up.
Car airbags
A chemical reaction produces gas that fills the bag in milliseconds, and the gas cools as it expands.
Baking
Gas bubbles in dough expand in the oven as they heat.
Lab gas collection
Chemists correct gas volumes measured at room conditions to standard conditions for comparison.
When Can You Use This Volume Calculator?
Use the combined gas law to find volume 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 temperature changes
You know P1, P2, T1, and T2.
Absolute units
Temperature is in Kelvin and pressure is absolute.
Volume Calculator vs Other Gas Law Tools
| Tool | Use It When | Formula |
|---|---|---|
| Volume Calculator (this page) | Pressure and temperature both change, and you need volume | V2 = (P1 × V1 × T2) / (P2 × T1) |
| Boyle's Law Calculator | Only pressure changes, temperature constant | P1V1 = P2V2 |
| Charles's Law Calculator | Only temperature changes, pressure constant | V1/T1 = V2/T2 |
| Gay-Lussac's Law Calculator | Pressure and temperature change, volume constant | P1/T1 = P2/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 volume from moles, or the amount of gas changes | PV = nRT |
Common Volume 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 ratio give a wrong answer | Convert P1 and P2 to one unit |
| Mixing volume units | mL and L in the same equation break the result | Convert to one unit and report in your chosen unit |
| Swapping P1 and P2 | Inverts the pressure ratio and the answer | Use P1/P2, not P2/P1, in the V2 formula |
| Swapping T1 and T2 | Inverts the temperature ratio | Use T2/T1 in the V2 formula |
| Forgetting the constant amount rule | Moles must not change | Use the ideal gas law if gas is added or lost |
| Ignoring water vapor | Gas collected over water includes vapor pressure | Subtract water vapor pressure first |
| 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 |
Volume Calculator FAQs
Frequently asked questions about calculating gas volume with the Combined Gas Law, molar volume at STP, and units.
How do you calculate final volume with the combined gas law?
Use V2 = (P1 × V1 × T2) / (P2 × T1). Convert temperatures to Kelvin, use matching units for both pressures, substitute the values, and solve.
What is the formula for volume in the combined gas law?
The formula is V2 = (P1 × V1 × T2) / (P2 × T1), which comes from rearranging P1V1/T1 = P2V2/T2.
Why must temperature be in Kelvin when calculating volume?
Gas volume 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 volume unit?
Yes, as long as the answer is read in the same unit as V1. Common choices are liters, milliliters, and cubic meters. The calculator converts them for you.
What happens to volume if pressure increases and temperature increases?
The two effects oppose each other. Higher pressure compresses the gas, and higher temperature expands it. Compare T2/T1 with P2/P1 to see which effect wins.
What happens to gas volume at absolute zero?
The straight-line relationship predicts zero volume at 0 K, but real gases condense into liquids or solids before that point, so the law stops applying.
Can I solve for volume 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.
What is the volume of one mole of gas at STP?
It is 22.414 L at 273.15 K and 1 atm, or about 22.711 L at 273.15 K and 100 kPa (the current IUPAC definition). Check which one your course uses.
How do I convert liters to milliliters or cubic meters?
Multiply liters by 1000 to get milliliters, or divide by 1000 to get cubic meters. For example, 2.5 L equals 2500 mL or 0.0025 m³.
Is the volume 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.
How is this different from the Charles's law calculator?
The Charles's law calculator assumes pressure is constant. This volume calculator handles cases where pressure and temperature both change.
Why does a balloon expand as it rises?
Atmospheric pressure drops with altitude, so the gas inside pushes the balloon outward until the internal and external pressures match. The falling temperature partly offsets this, but the pressure drop usually dominates.