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Charles's Law Calculator

Chemistry

Solve for any variable in Charles's Law (V₁/T₁ = V₂/T₂ at constant pressure). Select the unknown variable, enter the three known values, and choose your preferred units.

Quick Examples:

Calculator Settings

Input Values

Enter three known values — the field for the selected unknown is automatically calculated.

Absolute Temperature Required
Temperatures are internally converted to Kelvin. Inputs in °C or °F are accepted and converted automatically.

About This Tool

Charles's Law Calculator – Solve V₁/T₁ = V₂/T₂ Instantly

Charles's Law describes the direct relationship between the volume and absolute temperature of a fixed amount of ideal gas held at constant pressure. This free online Charles's Law calculator lets you solve for any one of the four variables — V₁, T₁, V₂, or T₂ — when the other three are known, with automatic unit conversion and step-by-step solutions.

Whether you are a chemistry student, teacher, or engineer, this tool handles the unit conversions automatically (°C/°F to Kelvin) so you can focus on understanding the science.

📘 What is Charles's Law?

Discovered by French physicist Jacques Charles in the 1780s and later formalized by Joseph Louis Gay-Lussac, Charles's Law states:

Charles's Law
V₁ / T₁ = V₂ / T₂  (at constant pressure)
Or equivalently: V / T = k (constant)

Where V₁ and T₁ are the initial volume and absolute temperature, and V₂ and T₂ are the final volume and absolute temperature. Because volume is directly proportional to temperature, doubling the absolute temperature exactly doubles the volume — and halving it halves the volume.

🌡️ Why Use Kelvin?

Gas laws require absolute temperature (Kelvin) because they model the average kinetic energy of gas molecules, which is proportional to the thermodynamic temperature. Kelvin starts at absolute zero (0 K = −273.15 °C), where gas molecules theoretically have zero kinetic energy. Using Celsius or Fahrenheit yields incorrect results because those scales have arbitrary zero points.

This calculator accepts °C and °F inputs and converts them to Kelvin automatically:

K = °C + 273.15
K = (°F − 32) × 5/9 + 273.15

⚙️ How the Calculator Works

To use the Charles's Law calculator:

  1. Choose which variable to solve for — V₁, T₁, V₂, or T₂.
  2. Enter the three known values and select their units.
  3. The calculator converts all temperatures to Kelvin and all volumes to m³, applies the formula, and converts the result back to your chosen units.
  4. View the step-by-step solution, the V/T proportionality constant, and the optional V vs T chart.

The four rearranged formulas used are:

V₂ = V₁ × (T₂ / T₁)
V₁ = V₂ × (T₁ / T₂)
T₂ = T₁ × (V₂ / V₁)
T₁ = T₂ × (V₁ / V₂)

🧮 Practical Examples

Example 1 — Hot Air Balloon: A balloon contains 1 000 L of air at 20 °C (293.15 K). The air is heated to 80 °C (353.15 K) at constant pressure. What is the new volume?

V₂ = 1 000 L × (353.15 K / 293.15 K) = 1 204.6 L

The balloon expands from 1 000 L to approximately 1 205 L — a 20.5% increase matching the 20.5% temperature increase on the Kelvin scale.

Example 2 — Bicycle Tire in Cold Weather: A tire has a volume of 2.5 L at 25 °C (298.15 K). Overnight the temperature drops to −5 °C (268.15 K). What is the effective volume at the lower temperature?

V₂ = 2.5 L × (268.15 K / 298.15 K) ≈ 2.252 L

The volume decreases to about 2.25 L — explaining why tires appear slightly deflated on cold mornings.

Example 3 — Finding the Required Temperature: A gas occupies 3.0 L at 27 °C (300.15 K). To what temperature must it be heated to expand to 4.0 L?

T₂ = 300.15 K × (4.0 / 3.0) = 400.2 K ≈ 127 °C

💡 Tips and Best Practices

Common Mistake
Always convert temperatures to Kelvin before applying Charles's Law. A temperature of 0 °C (273.15 K) is not absolute zero — using 0 °C directly would give a division by zero error.

Checking your answer: Verify that V/T₁ ≈ V₂/T₂ (the proportionality constant k should be the same on both sides). This calculator shows the V/T constant for quick verification.

Precision: Use at least 3 significant figures for temperatures in Kelvin. Since 1 °C difference at room temperature is only about 0.34% of absolute temperature, rounding errors can accumulate if you use too few decimal places.

Real gas limitations: Charles's Law applies accurately to ideal gases at moderate pressures and temperatures well above the liquefaction point. At very low temperatures near absolute zero or at high pressures, real gas deviations become significant.

🔗 Related Gas Laws

Charles's Law is one of the foundational gas laws that combine into the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) and ultimately the Ideal Gas Law (PV = nRT):

  • Boyle's Law (P₁V₁ = P₂V₂) — pressure–volume relationship at constant temperature.
  • Gay-Lussac's Law (P₁/T₁ = P₂/T₂) — pressure–temperature relationship at constant volume.
  • Ideal Gas Law (PV = nRT) — unifies all gas laws with the number of moles and the gas constant R.
  • Avogadro's Law (V ∝ n) — volume–amount relationship at constant temperature and pressure.

Use the temperature converter and volume converter tools if you need to pre-convert units before entering them, or use the built-in unit selectors in this calculator for seamless conversions.

Frequently Asked Questions

Is the Charles's Law Calculator free?

Yes, Charles's Law Calculator is totally free :)

Can I use the Charles's Law Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Charles's Law Calculator?

Yes, any data related to Charles's Law Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

What is Charles's Law?

Charles's Law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in Kelvin). This is expressed as V₁ / T₁ = V₂ / T₂. When temperature doubles, volume doubles; when temperature halves, volume halves.

How does this Charles's Law calculator work?

Select which variable you want to solve for (V₁, T₁, V₂, or T₂), enter the three known values with their units, and the calculator applies the formula V₁/T₁ = V₂/T₂. All temperatures are converted to Kelvin internally, then the result is converted back to your chosen unit. A step-by-step solution is shown for each calculation.

Why must temperature be in Kelvin for gas law calculations?

Gas law equations require absolute temperature (Kelvin) because they are based on the average kinetic energy of gas molecules, which is proportional to absolute temperature. Using Celsius or Fahrenheit would yield incorrect results because those scales have arbitrary zero points, not a true thermodynamic zero. Kelvin scale starts at absolute zero (0 K = −273.15 °C), where gas molecules theoretically have no kinetic energy.

What volume and temperature units are supported?

Volume units include L (litres), mL, m³, cm³, ft³, and in³. Temperature units include K (Kelvin), °C (Celsius), and °F (Fahrenheit). All temperatures are converted to Kelvin before calculation, and all volumes are converted to m³, then converted back to your selected unit for display.

What are some real-world examples of Charles's Law?

Common examples include: a balloon shrinking in cold weather (volume decreases as temperature drops), bread dough rising more in a warm kitchen, hot air balloons (heating air increases volume and reduces density for lift), and car tires appearing slightly deflated on cold mornings. Any scenario where a gas is heated or cooled at constant pressure follows Charles's Law.

What is the V/T proportionality constant shown in the result?

The V/T constant (k = V/T) remains the same for a given gas sample at constant pressure. For example, if k = 0.00335 m³/K, then at any temperature T, the volume is V = k × T. This confirms Charles's Law: the ratio V/T is invariant. The calculator shows k in m³/K (SI units).