Theis Well Drawdown Calculator
Drawdown in a confined aquifer at any distance and time from a well pumping at a constant rate, from the Theis non-equilibrium equation — with the well function W(u), the Cooper-Jacob straight-line check and the radius of influence.
For drawdown in the pumping well itself, enter the effective well radius as r — the result excludes well losses, so measured drawdown in a real well will be higher. Storativity is typically 10⁻⁵ to 10⁻³ for confined aquifers; for an unconfined aquifer use specific yield (≈0.05–0.30) only while drawdown is small compared with saturated thickness.
Well function W(u) table
| u | W(u) | u | W(u) |
|---|---|---|---|
| 1×10⁻⁴ | 8.633 | 0.1 | 1.823 |
| 1×10⁻³ | 6.332 | 0.5 | 0.5598 |
| 0.01 | 4.038 | 1 | 0.2194 |
| 0.05 | 2.468 | 5 | 0.001148 |
Worked examples
Example 1 — Interference at a neighbouring well (US)
Example 2 — The cone keeps growing
Example 3 — SI units
Drawdown versus distance
For Example 1 after one day, drawdown is 89.4 ft at r = 1 ft, 63.0 ft at 10 ft, 36.7 ft at 100 ft, 18.4 ft at 500 ft and 10.8 ft at 1,000 ft. Each tenfold increase in distance removes about the same drawdown while u stays small — the logarithmic shape that makes semi-log distance-drawdown plots straight lines.
References: Theis, C.V. (1935). "The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage." Trans. AGU 16, 519–524. Cooper, H.H., Jacob, C.E. (1946). Trans. AGU 27, 526–534. Abramowitz, M., Stegun, I.A. (1964). Handbook of Mathematical Functions, eq. 5.1.11 and 5.1.54. Driscoll, F.G. (1986). Groundwater and Wells, 2nd ed.
Related tools
- Darcy's law — groundwater flux and seepage velocity
- Soil permeability (k) by soil type
- Total dynamic head — add drawdown to the pump lift
- Pump brake horsepower
- Embankment seepage