Standardized Precipitation Index SPI Calculator

SPI standard-normal transform of an independently season/aggregation-matched precipitation CDF calibration. Zero-mass treatment and baseline completeness are caller verified; no automatic gamma fit or tail extrapolation. Caller independently establishes homogeneous observation coverage and model/reference applicability; not observed future climate, crop suitability or validated drought severity.

Description

A standardized precipitation index maps a calibrated probability onto a standard-normal scale.

A standardized precipitation index maps a calibrated probability onto a standard-normal scale.^[1]

Calibration period, accumulation duration and tail treatment must be established independently. Use Standardized Precipitation Index SPI Calculator to evaluate the supplied inputs under the model explained below.

When to use Standardized Precipitation Index SPI Calculator

Use Standardized Precipitation Index SPI Calculator to evaluate the supplied inputs under the model explained below. Establish the units, measurement scope and model assumptions before entering values.

How to use Standardized Precipitation Index SPI Calculator and understand its results

Establish the units, measurement scope and model assumptions before entering values.
Enter Independently calibrated precipitation coordinates, Independently calibrated precipitation cdf, Observed matched precipitation using the field table and validation rules below, then run the tool.
Read Conditional standard normal index, Matched cdf probability; interpret the units, signs, ordering and unknown-value placeholders described below.
Correct reported input errors and rerun. Apply successful results according to their specific meanings and check the assumptions before using them in a decision.

Input field	Meaning	Value type	Requirement
independentlyCalibratedPrecipitationCoordinates	Independently calibrated precipitation coordinates	array of number	Required; constraints below
independentlyCalibratedPrecipitationCdf	Independently calibrated precipitation cdf	array of number	Required; constraints below
observedMatchedPrecipitation	Observed matched precipitation	number	Required; constraints below

Enter at least two strictly increasing nonnegative precipitation coordinates with aligned nondecreasing CDF values from 0 to 1 and a nonnegative observation within the sampled range. Linearly interpolate the CDF, then apply the helper's rational approximation to the inverse standard-normal CDF. The interpolated probability must be strictly between 0 and 1; endpoint probabilities are errors rather than fabricated finite tail scores. The tool does not fit a distribution, select an accumulation period or add zero-rain mass.

p=interpolatedCalibratedCDF(observedPrecipitation); conditionalIndex=Φ⁻¹(p), requiring 0<p<1

Use the field order, units and branch conditions described above.

Output field	Meaning	Value type
conditionalStandardNormalIndex	Conditional standard normal index	number
matchedCdfProbability	Matched cdf probability	number

json

{
  "input": {
    "independentlyCalibratedPrecipitationCoordinates": [
      0,
      1,
      2
    ],
    "independentlyCalibratedPrecipitationCdf": [
      0.1,
      0.5,
      0.9
    ],
    "observedMatchedPrecipitation": 1
  },
  "output": {
    "conditionalStandardNormalIndex": 0,
    "matchedCdfProbability": 0.5
  }
}

Limitations and assumptions

Calibration period, accumulation duration and tail treatment must be established independently. Apply the exact scope and assumptions explained above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are explained above; extremely large inputs or outputs can also be rejected. Input errors differ from successful false results, empty match lists and unknown-evidence placeholders.

Alternative or Complementary methods

Use Standardized Precipitation Evapotranspiration Index SPEI Calculator for a related task: A standardized precipitation-evapotranspiration index uses a calibrated water-balance distribution.

Use Palmer Drought Severity Index Simplified Calculator for a related task: A simplified Palmer recurrence carries a previous state through monthly anomaly inputs.

References

Standardized Precipitation Index SPI Calculator — tool.io

Similar or alternative tools

Standardized Precipitation Evapotranspiration Index SPEI Calculator
A standardized precipitation-evapotranspiration index uses a calibrated water-balance distribution.
Palmer Drought Severity Index Simplified Calculator
A simplified Palmer recurrence carries a previous state through monthly anomaly inputs.