Flow Rate CalculatorQ = A × v · L/min · GPM
Volumetric flow rate is the volume of fluid passing a point per second: Q = A × v, the pipe’s cross-sectional area times the flow velocity. Find the flow in a pipe from its diameter and velocity, work out velocity from a known flow, measure a tap or pump with a bucket test, or set an IV infusion in mL/h and drops per minute.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Flow inputs
Use the inside diameter of the pipe, not the outside.
Step-by-step working
What is flow rate?
Flow rate is the volume of fluid that passes a given point per unit of time. It’s measured in cubic metres per second in SI, and more often in litres per minute, gallons per minute or millilitres per hour.
It’s used to size water pipes, pumps and irrigation, rate showers and taps, and in medicine to set intravenous infusions. Wherever it applies, the continuity principle holds: what flows in must flow out.
Quick answers
How do you calculate flow rate from pipe size?
Q = (π × d² ÷ 4) × velocity. A 25 mm pipe carrying water at 1.5 m/s moves 0.000736 m³/s, about 44.2 L/min.
How do I convert L/min to GPM?
Divide L/min by 3.785 for US gallons per minute. 100 L/min ≈ 26.4 US gpm. Multiply gpm by 3.785 to go back.
How do I calculate IV drip rate?
Drops per minute = volume (mL) × drop factor (gtt/mL) ÷ time (minutes). 1,000 mL over 8 hours with a 20 gtt/mL set is 41.7, rounded to 42 gtt/min.
How do I measure my tap or pump flow rate?
Time how long it takes to fill a bucket of known volume and divide: 10 L in 12 s is 50 L/min. Use the Bucket test tab, then check the pressure calculator if flow seems low.
Flow rate formulas
Continuity: in a closed pipe, Q stays the same, so the velocity rises wherever the pipe narrows (A₁v₁ = A₂v₂).
| Symbol | Meaning | SI unit |
|---|---|---|
| Q | Volumetric flow rate | m³/s |
| A | Cross-sectional area | m² |
| v | Mean flow velocity | m/s |
| d | Inside diameter | m |
| V, t | Volume collected and time | m³, s |
| gtt | Drops (from Latin guttae) | — |
How to calculate flow rate in a pipe
- Measure the inside diameter and convert it to metres.
- Find the area: π × d² ÷ 4.
- Multiply by the flow velocity (m/s) to get m³/s.
- Convert: × 60,000 for L/min, or × 15,850 for US gpm.
Worked example: water in a 50 mm pipe
Water flows at 2 m/s through a pipe with a 50 mm inside diameter.
Q = 0.0019635 × 2 = 0.003927 m³/s
= 235.6 L/min ≈ 62.2 US gpm
IV example: 1,000 mL over 8 h is 125 mL/h on a pump. On a 20 gtt/mL gravity set that’s 1,000 × 20 ÷ 480 = 41.7, about 42 drops per minute.
Typical flow rates
Rough figures for orientation.
| Source | Flow rate |
|---|---|
| Bathroom tap | 4–8 L/min |
| Low-flow shower head | 6–9 L/min |
| Garden hose (½″) | 15–25 L/min |
| Fire hose (2½″) | ≈ 950–1,900 L/min (250–500 gpm) |
| Adult maintenance IV | ≈ 80–125 mL/h |
IV drip rate quick table (drops per minute)
Gravity infusion rates for common volumes and times.
| Order | 10 gtt/mL | 15 gtt/mL | 20 gtt/mL | 60 gtt/mL |
|---|---|---|---|---|
| 1,000 mL / 8 h (125 mL/h) | 21 | 31 | 42 | 125 |
| 1,000 mL / 12 h (83 mL/h) | 14 | 21 | 28 | 83 |
| 500 mL / 4 h (125 mL/h) | 21 | 31 | 42 | 125 |
| 250 mL / 2 h (125 mL/h) | 21 | 31 | 42 | 125 |
Common mistakes to avoid
- Using the outside diameter. Wall thickness can cut the flow area a lot in small pipes.
- Forgetting to square the diameter. Doubling the diameter gives four times the area and flow at the same velocity.
- Mixing drop factors. A 60 gtt/mL microdrip set gives three times as many drops as a 20 gtt/mL set for the same mL/h.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who became a full-time tech geek, and I’ve spent 13+ years designing and coding web tools. IV flow rates and drop-factor maths are part of a pharmacist’s working life, so this calculator’s infusion mode follows the same formulas used on the ward. Its pipe-flow modes rest on the standard continuity equation.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Flow Rate Calculator: frequently asked questions
Volumetric flow rate Q = A × v, the cross-sectional area times the average velocity. For a measured volume, Q = V ÷ t.
Velocity is how fast the fluid moves (m/s). Flow rate is how much volume passes per second (m³/s). A wide, slow river can carry more than a narrow, fast stream.
At the same velocity, flow scales with diameter squared. At the same pressure, a larger pipe also has less friction loss, so flow rises even faster.
The number of drops that make 1 mL on a given IV administration set: 10, 15 or 20 gtt/mL for macrodrip and 60 gtt/mL for microdrip.
For an incompressible fluid, A₁v₁ = A₂v₂: whatever flows in must flow out, so narrowing a hose speeds up the water.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 14.5, Fluid Dynamics: flow rate and continuity
- HyperPhysics, Georgia State University — volume flow rate
- NCBI StatPearls — Intravenous Fluid Administration — IV infusion practice
Disclaimer: This calculator is an educational tool. IV rates must always follow a prescriber’s order and local clinical protocols, with independent double-checks. Pipe results assume full, steady flow.