Calculator
Example Data Table
| Initial Temp | Ambient Temp | k | Time | Final Temp |
|---|---|---|---|---|
| 95 °C | 22 °C | 0.08 | 15 | 44.00 °C |
| 180 °F | 70 °F | 0.05 | 20 | 110.47 °F |
| 360 K | 295 K | 0.03 | 25 | 325.70 K |
Formula Used
Newton law of cooling:
T(t) = Ta + (T0 - Ta)e-kt
Here, T(t) is final temperature. Ta is ambient temperature. T0 is initial temperature. k is the cooling constant. t is elapsed time.
Cooling constant: k = -ln((T - Ta) / (T0 - Ta)) / t
Elapsed time: t = -ln((T - Ta) / (T0 - Ta)) / k
Instant cooling rate: dT/dt = -k(T - Ta)
How to Use This Calculator
Choose the calculation type first. Enter the known temperature values. Add the ambient temperature. Enter the cooling constant when it is known. Add elapsed time when finding final temperature. Enter target temperature when finding time or k. Press submit to view the result above the form.
Use one temperature scale at a time. Do not mix Celsius and Fahrenheit. The model assumes stable ambient temperature. It also assumes the object cools evenly.
Understanding Newton Law of Cooling
What the Model Means
Newton law of cooling describes temperature change over time. It works when heat transfer is proportional to the temperature difference. The object moves toward ambient temperature. The curve is not linear. It is exponential. This makes the early cooling stage faster. Later cooling becomes slower.
Why the Constant Matters
The cooling constant is called k. A larger k means faster cooling. A smaller k means slower cooling. The value depends on surface area, material, airflow, insulation, and surrounding conditions. A hot drink in moving air cools faster. A covered cup cools slower.
Useful Physics Applications
This calculator helps with many physics tasks. It can estimate the temperature of water, food, metals, lab samples, and small objects. It is useful for classroom problems. It is also helpful for quick engineering checks. The tool can solve final temperature, elapsed time, cooling constant, and ambient temperature.
Using Reliable Inputs
Good inputs improve the result. Measure initial temperature carefully. Use a stable ambient temperature. Keep the same unit through the whole calculation. The time unit must match the cooling constant. If k is per minute, time should be in minutes. If k is per second, time should be in seconds.
Limits of the Equation
The formula is a simplified model. It does not handle changing room temperature. It does not include phase change. Boiling, freezing, evaporation, and radiation can affect real results. Large objects may cool unevenly. Strong airflow can also change k during the process.
Interpreting Results
The final temperature should move toward the ambient value. It should not pass the ambient value in normal cooling. If it does, check the signs and units. The calculated cooling rate shows how quickly temperature changes at that moment. It gets smaller as the object nears ambient temperature. Export the results when you need a record. Use the example table to compare common inputs.
FAQs
What is Newton law of cooling?
It is a physics model for temperature change. It says cooling rate depends on the difference between object temperature and ambient temperature.
Can this calculator find heating results?
Yes, it can model heating toward ambient temperature. Enter an initial temperature below the ambient temperature. The same exponential formula applies.
What is the cooling constant k?
The cooling constant measures how quickly an object approaches ambient temperature. A larger value means faster cooling or heating.
Can I use Fahrenheit?
Yes. Use Fahrenheit for all temperature inputs. Do not mix Fahrenheit with Celsius or Kelvin in the same calculation.
Why is my time result invalid?
The target temperature may be unreachable under the entered conditions. Check the ambient temperature, cooling constant, and target temperature.
Does this work for boiling water?
It can estimate cooling after boiling stops. Active boiling, evaporation, and steam loss can make the simple model less accurate.
What time unit should I use?
Use the time unit that matches k. If k is per minute, enter minutes. If k is per second, enter seconds.
Can I download the result?
Yes. Use the CSV or PDF buttons after entering values. The file includes inputs and calculated output.