Specific Heat Calculator

What is specific heat?

Specific heat capacity is a property of a substance that tells you how much energy it takes to raise the temperature of one kilogram of that substance by one kelvin (or, equivalently, by one degree Celsius). Water, for example, has a high specific heat of about 4186 J/(kg·K), which is why it warms up and cools down slowly compared with metals.

This calculator uses the fundamental heat equation $Q = m \cdot c \cdot \Delta T$ and lets you solve for any one of the four quantities: the heat energy $Q$, the mass $m$, the specific heat capacity $c$, or the temperature change $\Delta T$.

How does the calculator work?

Choose what you want to find from the “Calculate” menu, then enter the three known values. The calculator keeps everything in SI units internally — energy in joules (J), mass in kilograms (kg), specific heat in J/(kg·K), and temperature change in kelvin (K). A change of 1 K is exactly the same size as a change of 1 °C, so $\Delta T$ can be entered as either a temperature difference in kelvin or in degrees Celsius.

When solving for mass, specific heat, or temperature change, the calculator divides by the other quantities, so it returns no result if any divisor is zero.

Formula

The heat energy needed to change the temperature of a substance is:

Where:

• $Q$ is the heat energy added or removed, in joules (J),
• $m$ is the mass of the substance, in kilograms (kg),
• $c$ is the specific heat capacity, in J/(kg·K),
• $\Delta T$ is the temperature change, in kelvin (K).

Rearranging lets you solve for any unknown:

Worked examples

Example 1: Heating water

Heat 2 kg of water ($c = 4186 \, \text{J/(kg·K)}$) by 10 K. The heat energy required is:

So 83720 joules are needed.

Example 2: Solving for mass

Suppose 83720 J of heat raised the temperature of some water ($c = 4186 \, \text{J/(kg·K)}$) by 10 K. The mass is:

The sample had a mass of 2 kg, confirming the first example.

Practical notes

• Specific heat values vary with temperature and phase; published values are typically given near room temperature.
• The formula assumes no phase change (no melting or boiling). Crossing a phase boundary requires latent heat, which this calculator does not include.
• A negative $\Delta T$ (cooling) gives a negative $Q$, meaning heat is removed from the substance.

If you are studying gases, you may also find our air density calculator and Boyle’s law calculator useful.