Calculator Inputs
Example Data Table
| Well | X coordinate | Y coordinate | Measuring point elevation | Depth to water | Hydraulic head |
|---|---|---|---|---|---|
| MW-1 | 100 | 100 | 52.30 | 5.20 | 47.10 |
| MW-2 | 260 | 120 | 51.80 | 5.95 | 45.85 |
| MW-3 | 170 | 300 | 53.10 | 6.10 | 47.00 |
Formula Used
The calculator fits a hydraulic head plane through the three wells:
h = ax + by + c
The hydraulic gradient is the magnitude of the head slope:
i = √(a² + b²)
The vector (a, b) points toward increasing hydraulic head. Groundwater flow is normally reported in the opposite direction, so the flow vector is (-a, -b). Azimuth is measured clockwise from north.
How To Use This Calculator
Choose whether you want to enter direct hydraulic heads or calculate heads from elevation and depth to water. Enter X and Y coordinates for each well. Use the same horizontal coordinate system for all wells. Select units for coordinates and heads. Press the calculate button. Review the result panel above the form. Export the result when needed.
Understanding Three Well Hydraulic Gradient
A three well gradient method uses water level data from three separate wells. The wells form a triangle across the site. Each well gives one point on the potentiometric surface. When coordinates and hydraulic heads are known, the calculator fits a plane through those three points. The slope of that plane is the hydraulic gradient.
Why Three Wells Matter
Two wells can show a simple head drop along one line. They cannot define a full groundwater surface. Three wells define direction and steepness in two dimensions. This is useful during site investigations, plume tracking, pumping reviews, and drainage studies. Good spacing is important. Wells should not be nearly collinear. A wider triangle often gives a stronger direction estimate.
Main Inputs
The calculator can use direct hydraulic head values. It can also compute head from measuring point elevation and depth to water. Coordinates should use the same horizontal unit. Head values are converted when a different unit is selected. Names are optional, yet they make exports easier to read. The tolerance field checks whether the three wells are too close to a straight line.
Interpreting Results
The gradient magnitude is dimensionless when vertical and horizontal units match. A value of 0.005 means the head changes by five units over one thousand horizontal units. The azimuth of increasing head points uphill on the water table. Groundwater flow is normally reported in the opposite direction. The tool also lists the plane equation, pair gradients, triangle area, and a quality note.
Practical Guidance
Review field notes before accepting any result. Confirm measuring point elevations. Check that water levels were collected close together in time. Avoid mixing static readings with pumping influenced readings. Screen intervals should represent the same aquifer. If the computed direction conflicts with site geology, review the data and nearby boundaries. Use the export buttons to keep calculation evidence with your report.
Advanced Options
The advanced fields help standardize mixed field sheets. You can switch coordinate and head units, choose head entry style, and store map notes. The result panel keeps both the gradient vector and the flow vector visible. This helps reviewers see which direction was calculated and why. Use it as a screening tool.
FAQs
What is hydraulic gradient?
Hydraulic gradient is the change in hydraulic head divided by horizontal distance. It describes the slope of the groundwater surface and is usually dimensionless when both measurements use matching units.
Why are three wells needed?
Three wells define a plane in two dimensions. This lets the calculator estimate both gradient magnitude and flow direction across a site area.
Can I use feet and meters together?
Yes. Select coordinate and head units separately. The calculator converts head values to the coordinate unit before computing the dimensionless gradient.
What does flow azimuth mean?
Flow azimuth is the estimated groundwater flow direction. It is reported in degrees clockwise from north and points from higher head toward lower head.
What is the plane equation?
The plane equation represents hydraulic head as a sloping surface across X and Y coordinates. Its coefficients are used to compute gradient and direction.
What is a weak triangle warning?
A weak triangle warning means the wells are nearly aligned. Direction results can become unstable when three points do not form a useful triangle.
Should water levels be measured together?
Yes. Readings should be collected close together in time. Changing pumping, recharge, or tidal effects can distort the gradient if measurements are not comparable.
Can this replace professional interpretation?
No. It supports calculations and reporting. Field conditions, geology, well construction, and data quality still need professional review before final decisions.