Rainfall Depth from Intensity and Duration

This is the shortest formula in the shard and it closes the largest gap in the catalog. An IDF curve gives an intensity. The rational method consumes an intensity. But the curve-number method wants a storm depth, detention pond sizing wants a volume, and the soil-loss equation wants storm energy built from depths. $P = it$ is the whole of the bridge: 50 mm/h held for two hours is 100 mm of rain. That is it. The reason it deserves a page rather than a footnote is that the arithmetic is done wrong constantly, almost always by mixing a duration in minutes with an intensity per hour and losing the factor of 60. Name that failure precisely, because it is so ordinary: an intensity per hour multiplied by a duration in minutes comes out sixty times too large, and 6000 mm of rain looks obviously wrong while 100 mm does not, so the error survives review exactly when it is small enough to matter. Both quantities here carry their units, so the mistake cannot be made on this page.

The subtlety is which duration to use, and it is a real one. The intensity from an IDF curve is an AVERAGE over the duration it was read at — that is what the curve means. So $P = it$ is exact if and only if the $t$ you multiply by is the same $t$ you read the curve at. Read 100 mm/h off the curve at 15 minutes and you have 25 mm of rain, not 100 mm, and not whatever 100 mm/h would give over some other window. Read the curve at 6 hours and you get a much lower intensity but a much larger depth, because depth rises with duration while intensity falls. Two different durations answer two different design questions: the short one sizes the pipe, the long one sizes the pond.

Which brings up the thing the rational method quietly hides. It uses only the peak intensity at the time of concentration, so it never computes a volume at all, and it cannot tell you anything about storage. That is why anything with a pond in it moves to a curve-number or hyetograph method, and why the depth this page produces is the first input those methods need. One further caution when you carry the number forward: a constant-intensity block of rain is not a real storm. Real hyetographs are peaked, and a design storm distribution — the SCS Type II curve, the Chicago method, or your agency's own — redistributes the same total depth into a shape with a peak in it. That reshaping does not change $P$, which is the reassuring part, but it changes the peak flow and it changes the pond volume substantially. Use this page to get the depth right, then let the distribution decide when it arrives.