Drought Index Calculator (Palmer PDSI)
Apply the Palmer Drought Severity Index recursion to a monthly Z index, or build the Z index itself from a precipitation water balance, and read the resulting drought category.
🏜️ What is the Palmer Drought Severity Index?
The Palmer Drought Severity Index, universally shortened to PDSI, is a standardised number describing how far cumulative moisture supply has drifted from what a location normally needs. Wayne Palmer developed it for the US Weather Bureau in 1965, and it remains one of the most widely used drought metrics in the world. It typically ranges from about −4, meaning extreme drought, through zero for near-normal conditions, to about +4 for extremely wet, although exceptional multi-year events can push it well beyond either end.
What makes PDSI different from a simple rainfall deficit is that it is built on a water balance. Palmer's method first estimates how much precipitation the month should have received to keep evapotranspiration, soil recharge, runoff and soil moisture loss all at their long-term normal values. That quantity is called CAFEC precipitation, short for climatically appropriate for existing conditions. The gap between actual and CAFEC precipitation is the moisture departure, which is weighted by a climate-specific factor and then carried forward month after month with a memory term.
Drought monitors, agricultural agencies, water utilities and insurers all use PDSI operationally. In the United States it feeds directly into the US Drought Monitor and into federal crop disaster designations. Climate scientists use gridded PDSI reconstructions derived from tree rings to compare modern droughts with megadroughts that predate instrumental records, which is how researchers established that the early 2000s southwestern US drought was the driest multi-decade stretch in over a thousand years. Reinsurers use PDSI time series to price drought exposure in agricultural portfolios.
A frequent misconception is that PDSI reacts to individual storms. It does not, and that is deliberate. Because the recursion keeps 89.7 percent of last month's value, one very wet month typically lifts a deep drought by only a fraction of a point. Another misconception is that PDSI measures precipitation. It measures the balance between supply and demand, so a warm year with normal rainfall can still show drought because higher temperatures raise evapotranspiration demand. A third is that PDSI values are directly comparable to SPI or SPEI values, which they are not, because each index uses a different standardisation and a different effective timescale.
This calculator exposes both halves of the method. PDSI mode applies Palmer's monthly recursion directly to a Z index you already have. Z index mode builds that Z from a precipitation water balance first, then feeds it into the recursion, so you can trace the whole path from a rainfall total to a drought category.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A Severely Dry Month Deepens an Existing Drought
Previous PDSI = −1.50 (mild drought), this month's Z index = −3.46, projected 12 months
Example 2 — A Wet Month Starts a Slow Recovery
Previous PDSI = −3.20 (severe drought), this month's Z index = +2.10, projected 12 months
Example 3 — Building the Z Index from a Rainfall Shortfall
Actual precipitation 20 mm against CAFEC precipitation 75 mm, K = 1.6, previous PDSI = −1.50
Example 4 — A Wet Month in a Near-Normal Season
Actual precipitation 140 mm against CAFEC precipitation 80 mm, K = 1.2, previous PDSI = +0.40
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Palmer Drought Severity Index?
The Palmer Drought Severity Index (PDSI) is a standardised measure of cumulative moisture surplus or deficit, developed by Wayne Palmer in 1965 for the US Weather Bureau. It combines precipitation, temperature-driven evapotranspiration demand and a simple soil moisture model into a single number that typically ranges from about -4 (extreme drought) to +4 (extremely wet), with values near zero meaning near-normal conditions.
What formula does the PDSI recursion use?
Palmer's monthly recursion is X(i) = 0.897 times X(i-1) plus Z(i) divided by 3, where X is the PDSI and Z is that month's moisture anomaly index. The 0.897 duration factor carries most of the previous month's value forward, which is what gives PDSI its long memory, and the division by 3 scales the fresh monthly anomaly into the same units.
What is the Palmer Z index?
The Z index, or moisture anomaly index, is the climatic characteristic K multiplied by the moisture departure d, where d equals actual precipitation minus CAFEC precipitation. Unlike PDSI, Z has no memory of previous months, so it isolates how anomalously wet or dry a single month was relative to what that location and season normally require.
What is CAFEC precipitation?
CAFEC stands for climatically appropriate for existing conditions. It is the precipitation the month would have needed for evapotranspiration, soil recharge, runoff and soil moisture loss all to match their long-term normal values for that location and calendar month. It is computed as alpha times PE, plus beta times PR, plus gamma times PRO, minus delta times PL, where the Greek coefficients are long-term water balance ratios.
What PDSI value counts as a drought?
The standard Palmer classification is: -0.50 to -0.99 incipient drought, -1.00 to -1.99 mild drought, -2.00 to -2.99 moderate drought, -3.00 to -3.99 severe drought, and -4.00 or below extreme drought. Values between -0.49 and 0.49 are near normal, and the same bands mirror upward for wet spells, up to 4.00 and above for extremely wet.
What is the climatic characteristic K?
K is a weighting factor that converts a moisture departure in depth units into a comparable anomaly across different climates and seasons. Without it, a 50 mm shortfall in a wet tropical month and a 50 mm shortfall in an arid month would score the same, which would be misleading. Published monthly K values for most locations fall roughly between 0.5 and 3.
Why does PDSI change so slowly?
Because the recursion keeps 89.7 percent of last month's value, one month of exactly normal rainfall only shaves about 10 percent off an existing PDSI. Recovering from a PDSI of -3.0 to above -1.0 with normal precipitation alone would take roughly ten months. That memory is intentional: it reflects how slowly soil moisture, groundwater and reservoir storage actually recover.
Can PDSI go beyond the -4 to +4 range?
Yes. The -4 to +4 range describes typical extremes rather than hard limits. During exceptional multi-year events, PDSI values below -6 have been recorded. The projection table in this calculator can also run past -4 quickly, because it assumes the same severely negative Z index repeats every single month, which real weather almost never does.
What are the known limitations of PDSI?
PDSI uses a simplified two-layer soil model, treats all precipitation as rain, handles snowpack and frozen ground poorly, and responds to temperature only through potential evapotranspiration. It also has a fixed timescale of roughly nine to twelve months, so it can miss short flash droughts and long hydrological droughts alike. Self-calibrating PDSI and the SPEI were developed partly to address these gaps.
How does PDSI differ from SPI and SPEI?
SPI (Standardized Precipitation Index) uses precipitation only and lets you choose the timescale, from 1 month to 48 months. SPEI adds evapotranspiration demand to SPI while keeping the flexible timescale. PDSI adds a physical water balance and soil moisture memory but locks you into its own effective timescale. Drought monitors normally consult all three rather than relying on any one.
Why does this calculator ask for precipitation in millimetres but use inches internally?
Palmer developed the index in imperial units, so published values of the climatic characteristic K assume a moisture departure expressed in inches. To let you enter millimetres, which most of the world uses, the calculator divides the departure by 25.4 before multiplying by K. That keeps standard K values valid without any manual conversion.
Is a negative Z index always a drought?
Not by itself. A negative Z means the month was drier than climatically appropriate, but PDSI only enters a drought category once the accumulated deficit pushes the recursion below -0.50. One dry month applied to a PDSI of +2.0 might only bring it to +1.4, which is still a slightly wet reading.