Calculator Inputs
This form keeps the page in a single-column flow, while the fields shift to three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
Sample values below show a hot object cooling toward room temperature with T₀ = 90, Tₐ = 25, and k = 0.045.
| Time | Temperature | Ambient | Excess Over Ambient |
|---|---|---|---|
| 0 | 90.00 | 25.00 | 65.00 |
| 10 | 66.45 | 25.00 | 41.45 |
| 20 | 51.43 | 25.00 | 26.43 |
| 30 | 41.85 | 25.00 | 16.85 |
| 40 | 35.74 | 25.00 | 10.74 |
| 60 | 29.37 | 25.00 | 4.37 |
Formula Used
Newton’s cooling model states that the rate of temperature change is proportional to the difference between the object and ambient temperatures.
dT/dt = -k(T - Tₐ)
T(t) = Tₐ + (T₀ - Tₐ)e-kt
Temperature mode: Use T(t) = Tₐ + (T₀ - Tₐ)e-kt.
Time mode: Rearrange to t = -ln((Ttarget - Tₐ)/(T₀ - Tₐ)) / k.
Constant mode: Estimate k = -ln((Tobs - Tₐ)/(T₀ - Tₐ)) / tobs.
How to Use This Calculator
- Choose whether you want temperature, time, or cooling constant.
- Enter the initial temperature and the ambient temperature using the same unit.
- Provide the remaining values needed for the selected solve mode.
- Set decimal precision and optional chart end time if needed.
- Click Calculate Cooling to display the result above the form.
- Review the summary cards, detailed result table, generated curve, and time-series table.
- Download the result as CSV or PDF for records or reporting.
FAQs
1. What does the cooling constant represent?
The cooling constant measures how quickly the object approaches ambient temperature. Larger values mean faster cooling. It depends on material, geometry, airflow, and surrounding conditions.
2. Can I use Celsius, Fahrenheit, or Kelvin?
Yes. The formula works with any temperature unit if all temperatures use the same unit. Never mix units inside one calculation.
3. Why must target temperature lie between initial and ambient?
Newton’s law describes a smooth approach toward equilibrium. For cooling, the object moves from the initial temperature toward ambient, so a valid target must stay between them.
4. Why is ambient temperature never reached in finite time?
The exponential model approaches ambient temperature asymptotically. The difference becomes extremely small, but exact equality requires infinite time in the ideal model.
5. When should I solve for the cooling constant?
Use constant mode when you know the initial temperature, ambient temperature, observed temperature, and observed time. That lets you estimate k from real measurements.
6. Does this model work for heating too?
Yes. The same exponential equation describes approach to ambient from below as well. The calculator still works if the object starts colder than the surroundings.
7. What assumptions does this calculator make?
It assumes constant ambient temperature, a constant cooling coefficient, and a lumped object temperature. Strong phase changes or spatial temperature gradients reduce accuracy.
8. Why do results change when I alter chart end time?
The main result does not change. Only the plotted range and generated time-series table change, helping you inspect cooling behavior over a shorter or longer interval.