Newton Cooling and Target Time Calculator
Calculate exponential cooling or heating toward a fixed ambient temperature and determine when a target is reached.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply a constant-coefficient exponential to the difference from ambient. Invert that exponential only for target temperatures on the forward-time trajectory.
T(t)=Ta+(T0−Ta)e^(−kt); target time=−ln[(target−Ta)/(T0−Ta)]/k
Worked example
Initial 80°C, ambient 20°C and k=0.1 per minute give 42.0728°C at 10 minutes. Reaching 50°C takes ln2/0.1≈6.93147 minutes.
Assumptions and input details
A single uniform object temperature, constant ambient and positive constant k. The time entry and k must use reciprocal matching units. No phase change, internal thermal gradients or temperature-dependent heat-transfer coefficient. The model also heats an initially colder object toward ambient. Ambient is approached asymptotically; a target beyond it is unreachable. This is a thermal arithmetic model, not a food safety, process safety or storage recommendation.
References: OpenStax: exponential models and Newton cooling
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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