How this calculation works
Solve for the time to reach a target under exponential cooling or warming.
t=ln[(T₀−Tₐ)/(T−Tₐ)]/kA worked example
From 80 toward ambient 20, reaching 35 reduces the temperature difference by a factor of four.
Good to know
The target must lie between the start and ambient without reaching ambient exactly.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Solve for the time to reach a target under exponential cooling or warming.
The primary result is labeled “Elapsed time”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The target must lie between the start and ambient without reaching ambient exactly.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
From 80 toward ambient 20, reaching 35 reduces the temperature difference by a factor of four.
Which rule does this calculator apply?
t=ln[(T₀−Tₐ)/(T−Tₐ)]/k