Formula & Calculator
Water Quality Index (Simplified)
Combines multiple water quality parameters (pH, dissolved oxygen, turbidity, etc.) into a single weighted score describing overall water quality.
| Parameter | Weight (Wi) | Quality (Qi) |
|---|
Interpretation
WQI = Σ(Wi × Qi) / ΣWi. A weighted average of sub‑indices for multiple water quality parameters. Used to summarise overall water quality in a single number.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| WQI | Water quality index | |
| Wi | Weight assigned to parameter i | |
| Qi | Sub-index quality rating for parameter i (0-100) |
What it means
The Water Quality Index (WQI) is a simplified method to express the overall quality of water based on several measured parameters (e.g., dissolved oxygen, pH, nutrients). Each parameter is assigned a weight (Wi) representing its relative importance, and a sub‑index (Qi) based on its measured value relative to standards. The WQI is the weighted average of these sub‑indices. It is used to communicate water quality to the public and to compare the quality of different water bodies. Different WQI models exist, but the weighted sum approach is common. Example: Suppose three parameters have weights 0.4, 0.3, 0.3 and sub‑indices 80, 70, 90. WQI = (0.4×80 + 0.3×70 + 0.3×90) / (0.4+0.3+0.3) = (32+21+27)/1 = 80. This would be considered good water quality. WQI simplifies complex data but may lose some detail.
Worked example
Water Quality Index – Two Examples
Real‑World| Parameter | Value |
|---|---|
| DO | 80 (weight 0.3) |
| pH | 90 (weight 0.3) |
| Turbidity | 70 (weight 0.4) |
| Parameter | Value |
|---|---|
| DO | 95 |
| pH | 95 |
| Turbidity | 90 |
Common mistakes
- Wi: Weight assigned to each parameter (importance factor) – sum of Wi may or may not be 1.
- Qi: Sub‑index (quality rating) for each parameter – often between 0 and 100.
- Weighted average: The formula gives a weighted average score; if ΣWi ≠ 1, the result is a weighted sum divided by the sum of weights.
- Parameter selection: The choice of parameters and weights is subjective; use established WQI methods (e.g., NSF, CCME) for consistency.
- Interpretation: Higher WQI indicates better water quality; thresholds vary by method.
Applications
The simplified water quality index (WQI) aggregates multiple water quality parameters into a single score, using weighting factors (Wi) and sub‑index values (Qi) for each parameter. This index enables water resource managers to communicate overall water quality to the public and policymakers, to track trends, and to classify water bodies for different uses. WQI is applied to rivers, lakes, and groundwater, incorporating parameters such as dissolved oxygen, pH, temperature, and nutrients. While simplistic, this approach provides a transparent and interpretable measure of water quality. By using WQI, environmental agencies can prioritise restoration efforts, allocate resources, and evaluate the effectiveness of pollution control measures.
- Assessment of surface water quality for regulatory and public reporting
- Classification of water bodies for suitability (e.g., drinking, recreation, irrigation)
- Evaluation of watershed management and pollution control effectiveness
- Public education and citizen science initiatives
- Identification of water quality trends and problem areas
Frequently Asked Questions
The WQI is a single number that summarises the overall quality of water based on several parameters. The simplified formula is WQI = Σ(W_i × Q_i) / ΣW_i, where W_i is the weight (importance) of parameter i, and Q_i is the quality rating (score) for that parameter. Different WQI formulations exist.
Comparing WQI scores calculated with different parameter sets or weighting schemes as if they were directly comparable. Many different WQI formulations exist (e.g., US EPA, British Columbia, etc.), so they are not interchangeable.
Common parameters include:
- pH.
- Dissolved oxygen (DO).
- Biochemical oxygen demand (BOD).
- Chemical oxygen demand (COD).
- Total suspended solids (TSS).
- Ammonia, nitrate, phosphate.
- Fecal coliforms.
Each parameter has a rating curve based on its concentration. For example, DO may score 100 at ≥ 8 mg/L and 0 at ≤ 2 mg/L. The rating is usually linear or piecewise linear between guideline values.
Weights reflect the relative importance of each parameter for water quality. For example, DO might have a higher weight because it is critical for aquatic life. Weights are often determined by expert judgment or by the specific water use (drinking, recreation, etc.).
Σ(W_i × Q_i) = (0.2×80)+(0.2×70)+(0.1×90)+(0.3×60)+(0.2×85) = 16+14+9+18+17 = 74. ΣW_i = 1.0. WQI = 74/1 = 74.
Usually:
- Excellent: 90‑100.
- Good: 70‑89.
- Fair: 50‑69.
- Poor: 25‑49.
- Very poor: 0‑24.
- Subjective choice of parameters and weights.
- May not reflect toxicity or emerging contaminants.
- Does not capture synergistic effects.
- Can be misused for decision‑making without context.
Select parameters that are relevant to the designated use (e.g., drinking, aquatic life, recreation) and that are likely to be at risk. Include parameters for which regulatory standards exist. Consult with stakeholders and experts.
The Canadian WQI (CCME WQI) uses a different calculation: it considers the number of parameters that exceed guidelines, the frequency of exceedance, and the magnitude of exceedance. It is more robust but more complex. The simplified WQI is a weighted average of ratings.