Mann-Kendall trend test and Sen's slope calculator with change point and anomalies

What it does

Is a river’s flow falling? Are summers getting warmer at your station? Did air pollution drop after a new rule? These are trend questions, and the usual tools in climate, hydrology and environmental science are the Mann-Kendall test and Sen’s slope. Both use only the order of the values, not their exact size, so a few odd years or a skewed distribution do not throw them off, and they need no assumption that the trend is a straight line.

This tool runs the test, estimates how fast the values change with a confidence interval, looks for a single sudden change point (Pettitt test), and shows each value as an anomaly from a baseline period, like the warming stripes and bar charts in climate reports. Everything runs in your browser.

How to use it

1. Paste or open your series: a time column and a value column. Times can be years (1990), decimal years (1990.5), or dates such as 1990-07 or 1990-07-15. A single column of values works too. Gaps are fine; rows without a number are skipped.
2. Choose the test:
   • Mann-Kendall for independent values, such as annual totals.
   • Hamed-Rao correction when one year tends to resemble the next (persistence). It widens the uncertainty based on the autocorrelation of the detrended ranks. “First 3 lags” is the cautious version its authors suggested.
   • Seasonal Mann-Kendall for monthly data with a yearly cycle: each calendar month is compared only with the same month in other years.
3. Significance level: 5 % is usual. The slope’s confidence interval uses the matching confidence (95 %).
4. Unit and slope period: for yearly time, per decade is the common way to report climate trends.
5. Baseline: the years whose mean defines zero for the anomalies (climate services use 30-year periods such as 1991–2020).

What the results mean

• S counts how many later values are higher minus how many are lower. Z and the p-value say how unusual that would be with no trend. A p-value below your significance level means a significant trend.
• Kendall’s tau scales S to between −1 and +1.
• Sen’s slope is the median of the slopes between every pair of points. Its interval comes from the test’s variance (Gilbert’s method, interpolated between ranks).
• Change point: where the series splits into two parts with the most different levels. A significant change point and a significant trend can both describe the same data; look at the chart before deciding which story fits.

Worked example

The made-up series has 50 annual temperatures from 1975 to 2024. Mann-Kendall gives S = 480, Var(S) = 14,288.7 (with ties), Z = 4.01 and p = 6.1 × 10⁻⁵: a significant rise. Sen’s slope is +0.152 °C per decade (95 % interval +0.087 to +0.223), about +0.75 °C over the record. The series is persistent, so the Hamed-Rao correction multiplies Var(S) by 2.47 and the p-value rises to 0.011, still significant at 5 %. Pettitt places a change point between 2009 and 2010.

FAQ

How many values do I need? At least 10 for a meaningful test; with fewer, the confidence interval cannot be computed.

Does it handle ties? Yes, equal values reduce the variance with the standard correction.

Is it the same as a linear regression? No. Regression fits a straight line by least squares and is sensitive to outliers. Sen’s slope is a robust alternative and pairs naturally with Mann-Kendall.

Last updated 2026-11-08.