Water Quality Index (Simplified)

Parameters, weights and sub-indices

Each row is one water-quality parameter. W_i is its relative weight (the weights need not sum to 1 — the formula normalizes automatically). Q_i is the quality rating on the 0–100 scale, where 0 is pristine and 100 is severely degraded. Pick a preset, edit any row, or add and remove parameters.

Results

How the index is built

Each parameter contributes W_i·Q_i to the numerator. Those products are summed, then divided by the sum of the weights. Because the same ΣW_i is used in the denominator, the result is a weighted average of the Q_i values — it always lies between the smallest and largest Q_i you entered.

Contribution of each parameter

Bars show each parameter's share of the numerator Σ(W_i·Q_i). The longest bar is the parameter that dominates the index. Lowering the Q_i of a long bar moves the WQI the most.

WQI classification bands

This five-band scheme follows the widely used Brown–McClelland–Deininger formulation (1972) of the weighted arithmetic index, adopted by the U.S. National Sanitation Foundation and many national agencies.

Standard weights of the nine core parameters

Weights sum to 1.00 in this canonical set. Other agencies adjust the weights, add metals, or replace some parameters — the tool accepts whatever weights you supply, and normalizes by their sum automatically.

Key relations and unit conversions

Formula

• WQI: overall water quality index on the 0–100 scale (can exceed 100)
• W_i: relative weight assigned to parameter i
• Q_i: quality rating (sub-index) of parameter i, typically 0–100
• n: number of parameters included

Example — a moderately polluted river. Take nine parameters with the standard weights (DO 0.17, Fecal Coliform 0.16, pH 0.11, BOD₅ 0.11, Temperature 0.10, Total Phosphate 0.10, Nitrates 0.10, Turbidity 0.08, Total Solids 0.07) and sub-indices Q_i of 70, 75, 55, 75, 40, 70, 65, 72, 60 respectively. Then ΣW_i = 1.00 and Σ(W_i·Q_i) = 0.17·70 + 0.16·75 + 0.11·55 + 0.11·75 + 0.10·40 + 0.10·70 + 0.10·65 + 0.08·72 + 0.07·60 ≈ 65.4, giving WQI ≈ 65.4 — a "Fair" classification.

The index is a weighted average of the individual quality ratings, so it always lies between the smallest and largest Q_i. If all Q_i were equal to some value q, the WQI would be exactly q regardless of the weights. The weights only determine how strongly each parameter pulls the average toward its own rating.

The sub-index Q_i is not the raw measurement. Each parameter has its own rating curve that maps a physical value — mg/L of BOD, NTU of turbidity, percent saturation of DO — to a number between 0 and 100. Those curves are parameter-specific and are usually defined by the regulating agency: a pH of 7.5 might map to Q = 10, a pH of 5.0 to Q = 70, and a pH of 3.5 to Q = 100. The tool here accepts the Q_i directly, so you can use whatever rating curves your agency specifies. If you have raw measurements, look up or compute the Q_i first, then enter them.

Two properties of the weighted arithmetic form are worth noting. First, the average is compensatory: a very bad parameter can be partly hidden by several good ones. A river with excellent DO but very high fecal coliform might still return a "Fair" WQI because the other parameters pull the average back. A weighted geometric WQI, exp(Σ W_i ln Q_i / ΣW_i), is less compensatory and will punish any single very bad parameter more severely — some agencies prefer it for that reason. Second, because the denominator is ΣW_i, the weights are relative, not absolute. Doubling every weight leaves the WQI unchanged. Only the ratios between weights matter.

The index is only as good as the parameters and sub-indices that go into it. Adding more parameters improves representativeness but dilutes the influence of any single one; the choice of weights is a policy decision, not a physical law. The standard nine-parameter set and the weights shown above are the most widely cited starting point, but most agencies modify them for local conditions — adding heavy metals in mining districts, dropping temperature in tropical climates, replacing fecal coliform with E. coli where that is the measured indicator.

Advanced mode adds the per-parameter contribution fractions, the sensitivity ∂WQI/∂Q_i = W_i/ΣW_j, the range of the entered Q_i, and a target-WQI solver that shows what a single parameter's Q_i would have to become to reach a chosen WQI, holding the other parameters fixed.

References

• Wikipedia, Water quality index: history of the weighted arithmetic index and the classification bands
• Brown, R.M., McClelland, N.I., Deininger, R.A., O'Connor, M.F. (1972). A water quality index — crossing the physical barrier. Proceedings of the International Conference on Water Pollution Research, Jerusalem.
• NSF International: the original nine-parameter set and its rating curves
• WHO Guidelines for Drinking-water Quality: parameter significance and health limits
• NIST SP 811, Guide for the Use of the SI: unit conversion factors

How to Use This Tool

1. Pick a preset for the water body you have in mind, or start from the default nine parameters.
2. Edit the parameter names, weights and sub-indices. Add or remove rows as needed.
3. In Advanced, read the per-parameter contributions and the sensitivity column, and try the target-WQI solver.
4. Click Calculate WQI.
5. Read the classification band, then check the gauge, the contribution chart and the flow diagram.

What This Tool Offers

• Weighted arithmetic WQI = Σ(W_i·Q_i) / ΣW_i, with any number of parameters
• Editable parameter table with live Wi·Qi and running totals
• Five-band classification (Excellent, Good, Fair, Poor, Unsuitable)
• Colour-band gauge with a marker at the computed WQI
• Horizontal bar chart of each parameter's contribution
• Sensitivity ∂WQI/∂Q_i and target-WQI solver (Advanced)
• Presets for pristine stream, clean river, moderate, polluted urban, industrial and eutrophic lake
• Standard nine-parameter weight reference and full unit relations