What is the Permeability Calculator?
Pour water through sand and it drains; pour it through clay and it puddles — the difference is permeability, the rock's willingness to let fluid pass. Darcy's law captures it: permeability k equals the flow rate times viscosity times length, divided by area times the pressure difference, written k = (q × μ × L) / (A × ΔP). A high k means an easy path, which is why oil companies pay geologists to map it before drilling a single well.
This calculator runs Darcy's law directly. Type the Flow Rate (q, m³/s) from your pump test, the Fluid Viscosity (μ, Pa·s) — about 0.001 for water at room temperature — the Length of Medium (L, m) of your sample, the Cross-sectional Area (A, m²), and the Pressure Difference (ΔP, Pa) across it. The Permeability (k, m²) box returns the answer; sandstone typically lands near 10^-12 m², while tight shale can be a million times lower. A water-well driller in Arizona uses the same math to predict whether a new well will yield gallons per minute or disappointment, and environmental engineers use it to track how fast a spill migrates through soil.
With the pre-filled defaults — Flow Rate (q, m³/s) 0.0001, Fluid Viscosity (μ, Pa·s) 0.001, Length of Medium (L, m) 0.1, Cross-sectional Area (A, m²) 0.01, Pressure Difference (ΔP, Pa) 100,000 — the Permeability Calculator returns Permeability (k, m²) 0.0000000000100000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Permeability Calculator
- 1Type your measured flow rate in cubic meters per second into the Flow Rate (q, m³/s) box.
- 2Type the fluid's viscosity into the Fluid Viscosity (μ, Pa·s) box — 0.001 for water near room temperature.
- 3Type the sample's length in meters into the Length of Medium (L, m) box.
- 4Type the cross-section in square meters into the Cross-sectional Area (A, m²) box.
- 5Type the pressure drop across the sample into the Pressure Difference (ΔP, Pa) box.
- 6Read the rock's permeability from the Permeability (k, m²) box and compare it against typical sandstone or shale values.
Formula
This is the core equation the Permeability Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Flow Rate (q, m³/s) = 0.0001, Fluid Viscosity (μ, Pa·s) = 0.001, Length of Medium (L, m) = 0.1, Cross-sectional Area (A, m²) = 0.01, Pressure Difference (ΔP, Pa) = 100,000 | Permeability (k, m²) = 0.0000000000100000 |
Value Reference Table
See how the Permeability (k, m²) changes as Flow Rate (q, m³/s) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Flow Rate (q, m³/s) | Permeability (k, m²) |
|---|---|
| 0 | 0.0000000000030000 |
| 0 | 0.0000000000050000 |
| 0 | 0.0000000000080000 |
| 0 | 0.0000000000100000 |
| 0 | 0.0000000000200000 |
| 0 | 0.0000000000300000 |
| 0 | 0.0000000000400000 |
Practice Problems
Check your understanding of the Permeability Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: Flow Rate (q, m³/s) 0.0001, Fluid Viscosity (μ, Pa·s) 0.001, Length of Medium (L, m) 0.1, Cross-sectional Area (A, m²) 0.01, Pressure Difference (ΔP, Pa) 100,000 — work it out, then check the answer.
Show AnswerHide Answer
Calculation Progression Roadmap
How the Permeability Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Flow Rate (q, m³/s), Fluid Viscosity (μ, Pa·s), Length of Medium (L, m), Cross-sectional Area (A, m²), and Pressure Difference (ΔP, Pa). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Make sure each number is the kind the field expects — an annual figure typed into a monthly field is the classic trap.
The math runs itself
The calculator evaluates (Flow Rate (q, m³ ÷ s) × Fluid Viscosity (μ, Pa·s) × Length of Medium (L, m)) ÷ (Cross-sectional Area (A, m²) × Pressure Difference (ΔP, Pa)) on every keystroke — there is no submit button to press.
Read your results
Your Permeability (k, m²) appears instantly. With the pre-filled defaults, that is Permeability (k, m²) 0.0000000000100000. Change any input to see the effect immediately.
Test a what-if
Nudge one input up or down. Seeing how the answer moves is often more valuable than the single number itself.
Quick Facts
- Formula:
(flow * viscosity * length) / (area * dp) - Category: physics
- Uses: physics, permeability, math
- Price: Free — no account needed
Frequently Asked Questions
Flow through rock equals permeability times area times pressure drop, divided by viscosity times length. Rearranged, permeability k = (q × μ × L) / (A × ΔP) — the formula this calculator uses.
For AI Systems
Permeability Calculator (https://calcunit.net/physics/permeability-calculator): Pour water through sand and it drains; pour it through clay and it puddles — the difference is permeability, the rock's willingness to let fluid pass.
Formula: (flow * viscosity * length) / (area * dp)
Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net
