Well Drawdown Calculator
Solve the confined-aquifer Thiem equation for drawdown, pumping rate, transmissivity, or either radius — with a cone-of-depression diagram, aquifer-material presets, unit converters, and a radius-of-influence estimator.
Pumping rate (Q) ↑
Drawdown scales directly with Q — pump twice as fast and every point in the cone of depression drops twice as far, for the same aquifer and geometry.
Transmissivity (T) ↑
A more transmissive aquifer spreads the same pumping load over more of itself, so drawdown falls inversely with T — this is why a productive gravel aquifer barely dips for a well that would seriously stress a silty one.
Distance (r) — logarithmic, not linear
Drawdown depends on ln(R/r), so it falls off quickly near the well and much more gently farther out. Moving from 1 m to 10 m from the well removes as much drawdown as moving from 10 m to 100 m.
Radius of influence (R)
R sets where drawdown is defined to reach zero. Because it enters as ln(R), doubling R adds only ln(2) ≈ 0.693 to the log term — a real effect, but far gentler than a change in Q or T.
How to Use This Calculator
The Thiem equation links five quantities: drawdown s, pumping rate Q, transmissivity T, radius of influence R, and distance r. Pick which one to solve, then fill in the other four.
1. Choose what to solve for
Pick s, Q, T, R, or r from the "Solve for" buttons — the tool rearranges the formula automatically.
2. Pick a unit system
Metric (m³/day, m²/day, m) or US (gpm, ft²/day, ft) — every field converts together.
3. Set the aquifer material, or enter your own T
Use an illustrative preset, or — much better — enter a transmissivity from an actual pumping test.
4. Enter the other known values
Fill in Q, R and r (or whichever three remain), keeping R greater than r so the log term stays positive.
5. Read the result, steps, and diagram
The cone-of-depression diagram shows the shape of the drawdown curve for your numbers, from the well out to R.
6. Go Advanced, estimate R, or convert units
Advanced mode adds sensitivity and specific-capacity metrics; the radius-of-influence estimator and unit converters are further down the page.
What This Tool Offers
Built around the Thiem equation, the standard steady-state solution for radial groundwater flow to a well in a confined aquifer.
Solve any of five variables
Go from pumping and aquifer data to drawdown, or rearrange the same relation to find Q, T, R, or r.
Cone-of-depression diagram
A cross-section drawn from your actual numbers, showing the logarithmic drawdown curve between the well and the radius of influence.
Aquifer-material presets
Illustrative transmissivity presets from gravel down to clay, built from standard hydraulic-conductivity ranges.
Companion well metrics
Specific capacity, the log-ratio term, and transmissivity in alternate units, computed alongside every result.
Built-in sensitivity check
See how much drawdown moves for a ±1% nudge in Q, T, R, or r — and why distance behaves so differently.
Radius-of-influence estimator
Sichardt's empirical formula turns a drawdown-at-the-well and a hydraulic conductivity into an estimate of R, sendable straight into the calculator.
Reference Tables & Unit Conversions
Live converters, a radius-of-influence estimator, and sourced hydrogeology reference tables.
Flow-rate converter
Transmissivity converter
Radius-of-influence estimator (Sichardt)
Unit Conversion Factors
| Quantity | Conversion | Value |
|---|---|---|
| Flow rate | 1 m³/day | = 0.18345 gpm (US) = 0.011574 L/s |
| Flow rate | 1 gpm (US) | = 5.4511 m³/day |
| Length | 1 ft | = 0.3048 m |
| Transmissivity | 1 ft²/day | = 0.092903 m²/day |
| Transmissivity | 1 m²/day | = 10.7639 ft²/day = 80.52 gpd/ft |
| Transmissivity | 1 gpd/ft | ≈ 0.01242 m²/day |
Typical Hydraulic Conductivity by Material
| Unconsolidated material | Hydraulic conductivity K (m/s) |
|---|---|
| Gravel | 10⁻³ – 1 |
| Clean sand | 10⁻⁶ – 10⁻² |
| Silty sand | 10⁻⁷ – 10⁻³ |
| Silt, loess | 10⁻⁹ – 10⁻⁵ |
| Glacial till | 10⁻¹² – 10⁻⁶ |
| Unweathered marine clay | 10⁻¹² – 10⁻⁹ |
Source: Freeze & Cherry, Groundwater (1979), p. 29, as reproduced by LMNO Engineering. Hydraulic conductivity varies over roughly fourteen orders of magnitude across natural materials, so any single aquifer's value should be measured, not assumed.
Thiem Equation Reference & Related Formulas
| Quantity | Formula | Notes |
|---|---|---|
| Drawdown (confined) | s = (Q / 2πT) · ln(R/r) | This calculator; steady-state, fully penetrating well |
| Specific capacity | Q / s | Common measure of well performance/efficiency |
| Transmissivity from two obs. wells | T = Q · ln(r₂/r₁) / (2π(s₁−s₂)) | Standard Thiem method for analysing pumping-test data |
| Radius of influence (Sichardt) | R = 3,000 · sw · √K | R, sw in m; K in m/s; empirical, for a fully penetrating well |
| Drawdown (unconfined, Dupuit-Thiem) | H² − h² = (Q/πK) · ln(R/r) | Different governing equation — do not mix with the confined form above |
Sichardt's formula: Broward County environmental permitting guidance, citing Powers (1992); constant C = 3,000 for a fully penetrating well, or roughly 1,500–2,000 for a line of well points. It is a widely used empirical rule of thumb; some hydrogeology literature (e.g. the 2022 journal article "The Radius of Influence Myth") argues it lacks a rigorous physical basis, so treat R estimates from it as approximate.
Typical Transmissivity Classification
| T (m²/day) | General aquifer productivity |
|---|---|
| < 1 | Poor — usually unsuitable for a production well |
| 1 – 10 | Low |
| 10 – 100 | Moderate — small to medium domestic/community wells |
| 100 – 1,000 | Good — typical productive sand/gravel aquifers |
| > 1,000 | Very good to excellent — major municipal well fields |
Worked Calculation Reference
| Q (m³/day) | T (m²/day) | R (m) | r (m) | s (m) |
|---|---|---|---|---|
| 1,000 | 500 | 300 | 30 | 0.733 |
| 1,000 | 500 | 300 | 10 | 1.083 |
| 1,000 | 500 | 300 | 100 | 0.350 |
| 2,000 | 500 | 300 | 30 | 1.466 |
| 1,000 | 100 | 300 | 30 | 3.665 |
These rows are calculated directly from the formula on this page (not quoted from an external source) and can be used to check the calculator: doubling Q doubles s; cutting T to a fifth multiplies s by five.
What Is Well Drawdown?
When a well pumps water from a confined aquifer, it lowers the aquifer's pressure surface (the potentiometric surface) around it, forming a depression shaped like an inverted cone centered on the well — the "cone of depression." Drawdown is simply how far that surface has dropped at a given distance from the well. The Thiem equation is the classical steady-state solution describing exactly that shape, for the idealized case of a well fully penetrating a confined aquifer of constant thickness, pumped at a constant rate long enough for conditions to stabilize.
Thiem Equation
The defining relationship is:
Because the equation is algebraic once the logarithm is taken as given, it rearranges directly for the other variables:
T = Q · ln(R/r) / (2π · s)
R = r · e^(2πTs / Q)
r = R · e^(−2πTs / Q)
Thiem Equation Variables
| Symbol | Meaning | Typical unit |
|---|---|---|
| s | Drawdown at distance r | m (or ft) |
| Q | Constant pumping rate | m³/day (or gpm) |
| T | Aquifer transmissivity (K × thickness) | m²/day (or ft²/day) |
| R | Radius of influence (drawdown ≈ 0) | m (or ft) |
| r | Distance from the well to the point of interest | m (or ft) |
How Each Variable Affects Drawdown
Drawdown responds very differently to its four inputs. It's directly proportional to Q and inversely proportional to T — double the pumping rate or halve the transmissivity, and drawdown doubles either way. But its relationship with distance is logarithmic rather than linear: most of the total drawdown happens close to the well, and the curve flattens out steadily as r grows toward R. That's exactly the shape a cone of depression has in real aquifers.
Thiem Equation Calculation Examples
s = (1,000 / (2π × 500)) × ln(300/30) = 0.3183 × ln(10)
s = 0.733 m
T = Q · ln(R/r) / (2π s) = 800 × ln(5) / (2π × 0.5)
T = ≈ 410 m²/day
r = R · e^(−2πTs/Q) = 300 × e^(−2π×500×1/1000)
r = ≈ 12.96 m
Frequently Asked Questions
It assumes a homogeneous, isotropic, confined aquifer of constant thickness; a fully penetrating well pumped at a constant rate; steady-state (no longer changing with time) radial flow; and no recharge or boundaries within the radius of influence. Real aquifers rarely meet every assumption perfectly, which is why field results are treated as estimates.
Most commonly in reverse: pump a well at a known rate, measure the stabilized drawdown at two or more observation wells at different distances, and solve for transmissivity — the "Thiem method" of pumping-test analysis, shown in the reference table above.
R is rarely observed directly. Sichardt's empirical formula (R = 3,000 · sw · √K, with the estimator above) is a common rule-of-thumb starting point, though some hydrogeologists consider it a rough approximation rather than a physically rigorous result — see the note under the formula reference table.
Not directly. Unconfined aquifers follow the Dupuit-Thiem form instead, H² − h² = (Q/πK)·ln(R/r), because the saturated thickness itself changes as the water table drops. That's a different governing equation from the one on this page, shown in the reference table for comparison.
It falls out of solving the steady radial-flow (Darcy's law in cylindrical coordinates) differential equation: the cross-sectional area for flow grows with distance (as 2πr times thickness), so the hydraulic gradient — and therefore how fast the head recovers — naturally shrinks as 1/r, and integrating 1/r gives a natural logarithm.
Specific capacity is Q divided by s — the yield a well produces per unit of drawdown. It's a quick, practical measure of well performance and is shown as a companion metric in Advanced mode; a well with declining specific capacity over time may be silting up or losing efficiency.
What it means
The Thiem equation (or Thiem solution) gives the steady‑state drawdown (s) in a confined aquifer caused by pumping from a well. It assumes radial, steady flow and a fully penetrating well. The drawdown increases logarithmically with distance from the well and is proportional to the pumping rate. It is used in aquifer testing to determine transmissivity (T) from drawdown data. This equation is a classic in groundwater hydrology and is essential for well design, water supply planning, and environmental assessments. Understanding this helps hydrogeologists evaluate well performance and aquifer properties.
Worked example
Well Drawdown (Thiem Equation) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Q (m³/day) | 500 |
| T (m²/day) | 100 |
| R (m) | 300 |
| r (m) | 10 |
| Parameter | Value |
|---|---|
| Q | 1000 |
| T | 200 |
| R | 500 |
| r | 20 |
Common mistakes
- Thiem equation: s = (Q / (2πT)) · ln(R/r) – for steady‑state flow to a well in a confined aquifer.
- Drawdown s: The reduction in hydraulic head at the well – in metres.
- Q: Pumping rate – in m³/s.
- T: Transmissivity – in m²/s.
- R: Radius of influence – often estimated from observation wells.
- r: Well radius (or distance from well).
- Assumes: Fully penetrating well, steady‑state, confined aquifer, homogeneous.
Applications
The Thiem equation for well drawdown in a confined aquifer, s = (Q/(2πT))·ln(R/r), gives the drawdown (s) at a radial distance r from a pumping well, given pumping rate Q, transmissivity T, and radius of influence R. This is used to analyse pumping test data, to determine aquifer properties, and to design well fields. Hydrogeologists use it to estimate T and to predict drawdowns for proposed pumping schemes. By applying the Thiem equation, professionals can assess the feasibility of groundwater development, to avoid excessive drawdown, and to ensure sustainable yields. It is also applied in modelling well interference and in designing dewatering systems.
- Pumping test analysis for aquifer characterisation
- Wellfield design and optimisation of pumping rates
- Prediction of drawdown for environmental impact assessments
- Dewatering system design for excavations and mines
- Groundwater management and sustainable yield analysis
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