Quick answer
Flow rate Q = A × v, or volume ÷ time. A cross-section of 0.05 m² with a velocity of 2 m/s gives 0.1 m³/s, which is 100 L/s or 1,585 US gallons per minute.
Choose a mode, then enter area and velocity or volume and time. The calculator returns the flow in several units.
Related tools: Flow Rate Converter: Convert litres, gallons and cubic metres or feet per second, minute and hour. Reynolds Number Calculator: Reynolds number and flow regime in a pipe. Specific Gravity Calculator: Specific gravity from density, relative to water at 1,000 kg/m³.
How to use the Flow Rate Calculator
- Choose use: Area × velocity and Volume ÷ time.
- Optionally, enter cross-section area (m²) (above 0).
- Optionally, enter velocity (m/s) (above 0).
- Optionally, enter volume (L) (above 0).
- Optionally, enter time (s) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Use | Choose one: Area × velocity; Volume ÷ time | Starts at Area × velocity |
| Cross-section area (optional) | A number, in m² | > 0 |
| Velocity (optional) | A number, in m/s | > 0 |
| Volume (optional) | A number, in L | > 0 |
| Time (optional) | A number, in s | > 0 |
Formula and method
Formula
Q = A v = V ÷ t
IEEE-754 double precision; shown to the decimals indicated.
1 US gallon = 3.785411784 L.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Use = Area × velocity; Cross-section area = 0.05; Velocity = 2.
| Result | Value |
|---|---|
| Flow rate | 100 L/s |
| Cubic meters per second | 0.1 |
| US gallons per minute | 1,585.0323 |
Example 2
Inputs: Use = Volume ÷ time; Volume = 200; Time = 40.
| Result | Value |
|---|---|
| Flow rate | 5 L/s |
| Cubic meters per second | 0.005 |
| US gallons per minute | 79.2516 |
Example 3
Inputs: Use = Area × velocity; Cross-section area = 0.0123; Velocity = 1.5.
| Result | Value |
|---|---|
| Flow rate | 18.45 L/s |
| Cubic meters per second | 0.01845 |
| US gallons per minute | 292.4385 |
The first line is the headline result (flow rate). Below it the flow Rate Calculator lists cubic meters per second and uS gallons per minute, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Unit conversions
1 m³/s = 1,000 L/s = 15,850 gallons per minute. So 0.1 m³/s = 100 L/s = 1,585 gpm. Only the fields for the chosen mode are used.
Continuity
For an incompressible fluid, A₁v₁ = A₂v₂: if a pipe narrows to half the area, the velocity doubles. This is why a thumb over a hose speeds up the jet.
How the result changes with cross-section area
Holding every other input at the first worked example, this table changes only cross-section area. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Cross-section area | Flow rate | Cubic meters per second | US gallons per minute |
|---|---|---|---|
| 0.025 | 50 L/s | 0.05 | 792.5162 |
| 0.05 | 100 L/s | 0.1 | 1,585.0323 |
| 0.1 | 200 L/s | 0.2 | 3,170.0646 |
| 0.2 | 400 L/s | 0.4 | 6,340.1293 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Cross-section area: left empty shows "Enter the area." beside that field and no result.
- Time: left empty shows "Enter the time." beside that field and no result.
Choosing between the Flow Rate Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Flow Rate Converter](/converters/fuel-flow-rate-conversion-calculator/) | value, from and to | US gallon per minute (GPM) → Litre per minute (L/min) |
| [Reynolds Number Calculator](/science/reynolds-number-calculator/) | fluid density, flow velocity and pipe diameter | Reynolds number |
| [Specific Gravity Calculator](/science/specific-gravity/) | density | Specific gravity |
| [Water Viscosity Calculator](/science/water-viscosity/) | temperature | Dynamic viscosity |
| [Water Velocity Calculator](/science/water-velocity-calculator/) | flow and inside diameter | Velocity |
Background: fluid flow
Volumetric flow rate is Q = A × v (cross-sectional area times average velocity). Bernoulli's equation, P + ½ρv² + ρgh = constant, holds along a streamline for steady, incompressible, frictionless flow, so real pipes need friction corrections. The Reynolds number Re = ρvL/μ compares inertia with viscosity.
Laminar flow in a pipe is usually quoted below Re of about 2,100 to 2,300 and fully turbulent above about 4,000, with an uncertain transition between; treat the thresholds as approximate.
Assumptions and limitations
- Only the fields for the chosen mode are used
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for cross-section area and time to confirm this.
Frequently asked questions
How do I find velocity from flow?
Rearrange Q = A·v to v = Q ÷ A: 0.1 m³/s through 0.05 m² moves at 2 m/s.
What is volumetric flow rate?
Volume per unit time.
Does it apply to gases?
Yes, at constant density.
What does the Flow Rate Calculator calculate?
Volumetric flow rate from area and velocity, or volume and time. It returns Flow rate, Cubic meters per second and US gallons per minute.
What formula does the Flow Rate Calculator use?
Q = A v = V ÷ t. 1 US gallon = 3.785411784 L.
What do I need to enter in the flow Rate Calculator?
You enter Use. Optional: Cross-section area (m²), Velocity (m/s), Volume (L) and Time (s).
What does the “Use” option change?
It sets how the flow Rate is worked out. The choices are Area × velocity and Volume ÷ time.
What is an example of a flow Rate result?
With use Area × velocity, cross-section area 0.05 and velocity 2, the flow rate is 100 L/s.
Related calculators
- Flow Rate Converter — Convert litres, gallons and cubic metres or feet per second, minute and hour.
- Reynolds Number Calculator — Reynolds number and flow regime in a pipe.
- Specific Gravity Calculator — Specific gravity from density, relative to water at 1,000 kg/m³.
- Water Viscosity Calculator — Dynamic viscosity of liquid water at a temperature.
- Water Velocity Calculator — Water velocity in a pipe from flow and inside diameter.
- Pressure Calculator — Pressure from force and area, with unit conversions.
- Recycling Rate Calculator — Share of waste that is recycled or diverted.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.