Annual Peak Flow Sample Statistics Calculator
Flood frequency analysis starts by summarizing the record of annual peak flows at a gauge with a few sample statistics. This calculator takes an annual peak flow series and returns the number of values n, their sum, the mean, the standard deviation S, the coefficient of variation V and the skew coefficient G, together with the table of normalized deviations used to compute them.
The method follows Section 5.1.5 of FHWA HDS-2 Highway Hydrology. The mean is X̄ = ΣXi / n (Eq. 5.8). Each value gives a normalized deviation di = Xi / X̄ − 1. The standard deviation is S = X̄ √(Σdi2 / (n − 1)) (Eq. 5.9), the coefficient of variation is V = S / X̄ (Eq. 5.10) and the skew coefficient is G = n Σdi3 / ((n − 1)(n − 2) V3) (Eq. 5.11). All sums use unrounded terms in double precision.
The data field is preloaded with the 29 annual peaks of Mono Creek, California, from Example 5.3 and Table 5.5 of the same manual; the calculator reproduces n = 29, a sum of 30,672, a mean of 1058, S = 327, V = 0.3092 and G = −0.1879. Replace them with your own series to get its statistics.
Calculator
Used as a label only; no conversion is applied.
Separate values with new lines, spaces or commas. Use a decimal point. Every value must be a number above 0; at least 2 values.
- Number of values n
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- Sum ΣXi (ft³/s)
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- Mean X̄ (ft³/s)
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- Standard deviation S (ft³/s)
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- Coefficient of variation V (dimensionless)
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- Skew coefficient G (dimensionless)
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| # | Xi (ft³/s) | Xi / X̄ | di | di2 | di3 |
|---|---|---|---|---|---|
| Total | — | — | — |
How to use the calculator
- Choose the flow unit of your data, ft³/s or m³/s. It only labels the results; the numbers are not converted.
- Type or paste the annual peak flows into the text field, separated by new lines, spaces or commas, using a decimal point.
- The results update as you type; you can also press Calculate. Any value that is not a number above 0 is named in an inline message and no result is shown.
- Read n, the sum, the mean X̄, the standard deviation S, the coefficient of variation V and the skew coefficient G, all to 4 significant figures.
- Check the table of normalized deviations: its total row gives ΣXi, Σdi2 and Σdi3, the sums behind Eq. 5.8, 5.9 and 5.11.
Frequently asked questions
What are the normalized deviations di in the table?
Each annual peak Xi is divided by the sample mean and 1 is subtracted: di = Xi / mean − 1. The sums of di squared and di cubed, taken over unrounded terms, give the standard deviation (Eq. 5.9) and the skew coefficient (Eq. 5.11).
Why is the skew coefficient shown as not defined?
Eq. 5.11 divides by (n − 1)(n − 2)V³, so G needs at least 3 values and a coefficient of variation V above 0. With 2 values, or when every value is the same, G is shown as not defined and the other statistics are still reported.
Does the flow unit selector convert my data?
No. The selector only labels the results. The sum, mean and standard deviation are in the unit of the values you enter; the coefficient of variation V and the skew coefficient G are dimensionless.
Does this calculator give a design discharge?
No. It gives sample statistics of the annual peak flow series only. Regional or weighted skew and log transforms are not computed, and the skew coefficient is sensitive to small samples and extreme values.
Disclaimer
The results are an estimate only and are not a substitute for the judgment of a qualified engineer.
The method is Section 5.1.5 of FHWA HDS-2 Highway Hydrology, 3rd edition, FHWA-HIF-24-007, Eq. 5.8 to 5.11, p. 76, with Example 5.3 and Table 5.5 (Mono Creek, California), pp. 77-78.
The skew coefficient is sensitive to small samples and extreme values. Regional or weighted skew and log transforms are not computed. This page gives sample statistics, not design discharges.