Standardized Precipitation Index Calculator

Estimate monthly distribution-based SPI from consecutive precipitation data, or calculate a precipitation z-score from a mean and standard deviation. Daily-window comparisons are experimental standardized scores, not operational SPI.

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Standardized Precipitation Index Formula

The Standardized Precipitation Index (SPI) is computed by converting the cumulative probability of an observed accumulated precipitation amount to a standard normal value (dimensionless). A common approach fits a gamma distribution to accumulated precipitation totals and then applies a normal (Gaussian) inverse CDF transform.

SPI = Phi⁻¹(H(P)), H(P) = q + (1 - q) G(P;α,β)

Variables:

SPI is the Standardized Precipitation Index (dimensionless; standard normal units)
P is the accumulated precipitation over the chosen timescale (any consistent unit, e.g., mm)
G(P; α, β) is the gamma cumulative distribution function (CDF) evaluated at P with shape α and scale β (fit from a long-term record for the same timescale)
q is the probability of zero precipitation for that timescale (fraction of accumulated totals equal to 0 in the record), used because the gamma distribution is defined for P > 0
Φ⁻¹(·) is the inverse CDF of the standard normal distribution

Note: If you only standardize using a mean and standard deviation, z = (P − mean)/SD, you are computing a z‑score (standardized precipitation anomaly). This can be a rough proxy in some contexts, but it is not the formal SPI distribution-based method.

What is a Standardized Precipitation Index?

The Standardized Precipitation Index (SPI) is a meteorological index used to quantify precipitation deficits (drought) and surpluses (wetness) over a specified accumulation period (e.g., 1-, 3-, 6-, 12-month). SPI is derived by fitting a probability distribution to long-term precipitation totals for that accumulation period, converting an observed total to a cumulative probability, and transforming that probability to a standard normal value. Negative SPI values indicate drier-than-typical conditions, while positive values indicate wetter-than-typical conditions.

How to Calculate Standardized Precipitation Index?

The following steps outline how SPI is typically calculated.

Choose a timescale (e.g., 3-month SPI), supply consecutive monthly values and identify the first value’s calendar month. The calculator fits only accumulated totals ending in the latest calendar month across years. Any entered target must cover that same season and accumulation period. About 30 or more matching years is recommended; shorter records have weaker confidence.
Fit an appropriate probability distribution to the matching seasonal totals. Gamma uses an approximate maximum-likelihood fit to positive totals and a zero-mass correction H(0) = q. Pearson III uses a three-parameter sample-moment fit. Distribution fit and baseline quality still require separate assessment; empirical ranks and normal anomalies are explicitly labeled alternatives.
For the observed accumulated precipitation amount P, compute the cumulative probability H(P) (including q for zero precipitation, if applicable).
Transform H(P) to the standard normal scale using the inverse normal CDF: SPI = Φ⁻¹(H(P)).
Interpret SPI values (negative = drier than typical; positive = wetter than typical). Many references classify SPI using thresholds such as ±1, ±1.5, and ±2.
If you only have a long-term mean and standard deviation (not the full record), you can compute a standardized precipitation anomaly (z‑score) as an approximation, but it is not the formal SPI computation.

Example Problem (Z-score approximation):

Use the following variables as an example problem to test your knowledge of the z‑score approximation.

Accumulated precipitation for the chosen period (P) = 120 mm

Long-term mean for the same period = 80 mm

Long-term standard deviation for the same period (SD) = 20 mm

Standardized value (z) = (120 − 80) / 20 = 2.00

Standardized Precipitation Index Calculator screenshot