Christiansen Uniformity Calculator
Enter four measurement-point application depths; the tool computes Christiansen's uniformity coefficient CU = 100·(1 − Σ|xᵢ−x̄| ÷ (n·x̄)), assessing sprinkler/micro-irrigation water uniformity.
Input Data
Results
At a glance:Enter four measurement-point application depths; the tool computes Christiansen's uniformity coefficient CU = 100·(1 − Σ|xᵢ−x̄| ÷ (n·x̄)), assessing sprinkler/micro-irrigation water uniformity.
Formula
CU (%) = 100 × (1 − Σ|xᵢ − x̄| ÷ (n × x̄)).
$$CU = 100\left(1 - \dfrac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n\,\bar{x}}\right)$$How to Use
- Enter the depths measured at the four catch-cup points.
- The calculator returns the mean depth and CU.
Christiansen uniformity coefficient grading
| CU (%) | Grade | Note |
|---|---|---|
| ≥ 90 | Excellent | Very uniform application, high efficiency |
| 85–90 | Good | Design target for most precision irrigation |
| 75–85 | Fair | Room for improvement |
| < 75 | Poor | Large dry/wet variation, water waste, uneven crops |
| This example 92 | Excellent | [24,26,22,28] mm, mean 25 |
CU uses all points' absolute deviation from the mean; complementary to DU, which looks only at the lowest quarter.
FAQ
What CU is considered acceptable?
Common grading: CU ≥ 90% excellent, 85–90% good, 75–85% fair, below 75% poor. Most precision-irrigation design targets above 85%. Drip/micro-irrigation supplies point by point, usually achieving higher uniformity; sprinklers are more affected by spacing and wind and tend to score lower.
How is CU different from distribution uniformity (DU)?
CU measures overall dispersion using 'absolute deviation of all points from the mean', sensitive to whole-field variation; DU (low-quarter distribution uniformity) looks only at 'mean of the lowest quarter ÷ field mean', emphasizing how well the driest zone is satisfied. For the same data, DU is usually lower than CU. They are complementary: CU sees overall consistency, DU sees the worst zone; read both.
Why does low uniformity waste water?
Because to let the driest spot also meet crop water need, you must raise the whole-field application. The worse the uniformity and the larger the dry/wet gap, the more excess water is applied on wet zones — mostly lost as deep percolation or runoff, lowering irrigation efficiency, while uneven supply makes crop growth and yield uneven.
What usually causes low CU?
Common causes: sprinkler spacing too large or poorly arranged (insufficient overlap), insufficient system pressure or large pressure drop along the line, worn or partly clogged nozzles, and wind blowing water off-target during irrigation. Remedies are: redesign spacing and overlap, add pressure-regulating zones or larger pipes, periodically service/replace nozzles, and avoid strong-wind periods or use wind-resistant nozzles.
How many catch cups are reliable?
More and more regular is better; field sprinkler tests often lay out dozens of cups in a grid. This tool uses 4 representative points to illustrate the CU principle; with few points it is more sensitive to extremes and less representative. For a formal assessment, increase the number per standard specifications and record pressure, wind speed, and run time, measuring under repeatable conditions.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.