EngineeringFormulaFluid Mechanics
Flow Rate Calculator
Single-section volumetric flow calculator using Q = A v to solve flow rate, flow area, average velocity, or circular-pipe inside diameter.
Volumetric flow rate tells you how much fluid volume passes a section per unit time. This page is intentionally a single-section Q = A v calculator, where Q is volumetric flow rate, A is cross-sectional flow area, and v is average velocity through that section. It covers both direct-area problems and circular-pipe inside-diameter problems, so it handles the most common area-velocity flow questions without pretending to be a pressure-loss, viscosity-based, or fill-time flow model.
A · Internal cross-sectional flow area measured normal to the fluid path.
v · Average bulk speed through the known flow section.
Direct-area mode uses a known internal section area and average bulk velocity. If you only know a circular bore, switch to Circular Pipe mode instead of converting area by hand. If you only know collected volume and elapsed time, use Q = V/t instead of this page.
Solution
Enter the required values to calculate flow rate.
Q = A v
Formula Sheet
- QFlow Rate
- AFlow Area
- dInside Diameter
- vAverage Velocity
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Q | Flow Rate | Volumetric flow rate passing through the selected section. | L/min, m³/h, US gpm |
| A | Flow Area | Internal cross-sectional area normal to the flow direction. | cm², m², in² |
| d | Inside Diameter | Internal diameter of a circular pipe or duct used to compute cross-sectional flow area. | mm, in, ft |
| v | Average Velocity | Average bulk flow speed through the chosen section, not local peak centerline velocity. | m/s, ft/s, mph |
How to Use This Calculator
- 01Choose the geometry basis first. Use Direct Area when you already know the internal flow area. Use Circular Pipe when the section is round and you know or want the inside diameter instead.
- 02Select which quantity to solve for: flow rate, area or inside diameter, or average velocity.
- 03Enter the other two values with any supported units. The calculator converts them to coherent SI units internally before solving.
- 04For circular-pipe mode, enter the internal flow diameter, not nominal pipe size or outside diameter.
- 05If your data comes from collected volume over time, use Q = V/t directly instead of this page. This tool is specifically for area-velocity relationships.
- 06Use average bulk velocity for the section. If you are comparing two different sections of the same incompressible stream, the Continuity Equation Calculator is usually the better tool.
How the Formula Works
Volume flow rate is defined as Q = dV/dt. For a section of fluid moving through a uniform cross-section, that becomes Q = A v, where A is the cross-sectional area and v is the average speed through that section.
If the section is circular, the internal flow area is A = π d² / 4, so the same relationship can be written as Q = (π d² / 4) v. Rearranging those equations lets the calculator solve for flow rate, required area or diameter, or average velocity.
Worked Example 01
Flow rate from direct area and average velocity
Known
- Flow Area (A): 80 cm²
- Average Velocity (v): 2.5 m/s
Formula
Q = A v
Substitution
Q = 0.008 x 2.5
Result
Q = 0.02 m³/s (72 m³/h)
An internal flow area of 80 square centimeters carrying fluid at an average speed of 2.5 meters per second gives 0.02 cubic meters per second of volumetric flow.
Worked Example 02
Required direct area for a target flow and velocity
Known
- Flow Rate (Q): 1200 L/min
- Average Velocity (v): 1.5 m/s
Formula
A = Q / v
Substitution
A = 0.02 / 1.5
Result
A ≈ 0.01333 m² (133.3 cm²)
To carry 1200 liters per minute at 1.5 meters per second, the section needs about 0.01333 square meters of internal flow area.
Worked Example 03
Circular-pipe inside diameter from flow and velocity
Known
- Flow Rate (Q): 50 m³/h
- Average Velocity (v): 2 m/s
Formula
d = √(4 Q / (π v))
Substitution
d = √(4 x 0.01389 / (pi x 2))
Result
d ≈ 0.0940 m (94.0 mm)
If the target flow is 50 cubic meters per hour and the average velocity limit is 2 meters per second, a circular internal diameter of about 94 millimeters is required.
Applications
- 01Estimating how much liquid or gas volume passes through a pipe, duct, or channel at a known average velocity
- 02Sizing the required internal flow area or pipe diameter to keep velocity within a target operating range
- 03Back-checking whether a reported flow rate and pipe size imply a realistic average bulk velocity
Circular Pipe Quick Reference at 1 m/s Average Velocity
| Inside Diameter | Flow Area | Flow Rate at 1 m/s |
|---|---|---|
| 25 mm | 4.91 cm² | 29.5 L/min |
| 50 mm | 19.63 cm² | 117.8 L/min |
| 75 mm | 44.18 cm² | 265.1 L/min |
| 100 mm | 78.54 cm² | 471.2 L/min |
Assumptions
- 01The entered velocity is an average one-dimensional section velocity suitable for Q = A v calculations.
- 02Circular mode assumes a fully circular internal flow section and uses the inside diameter to derive area.
- 03The tool evaluates a single section of flow and does not model losses, compressibility effects, or velocity-profile details.
Where This Model Stops
- 01Not a general all-method flow-rate page. It does not solve collected-volume-over-time workflows or pressure-driven flow from pressure drop, viscosity, roughness, or pipe length; use Q = V/t directly or a Darcy-Weisbach, Hazen-Williams, or Poiseuille-style model when those inputs define the problem.
- 02Does not calculate mass flow rate directly. If density matters, convert volumetric flow to mass flow separately using m-dot = rho Q.
- 03Not intended for compressible nozzle or gas-dynamics problems where density changes materially along the section or between stations.
References
- [1]14.5 Fluid Dynamics
OpenStax University Physics Volume 1
Defines volumetric flow rate and derives Q = A v, then connects it to the incompressible continuity equation.
- [2]Conservation of Mass
NASA Glenn Research Center
Explains mass conservation in flowing fluids and shows that density, area, and velocity combine into the continuity relationship.
- [3]Lecture 3: Continuity Equation
MIT Fluid Modules
Derives the continuity equation from conservation of mass and identifies the incompressible special case used in practical engineering flow calculations.
Frequently Asked Questions
Is this the same as the continuity equation calculator?
They are related but not identical in intent. This page solves the single-section relationship Q = A v, or the circular-pipe form based on inside diameter. The Continuity Equation Calculator compares two different sections of the same incompressible flow path using A1v1 = A2v2.
Should I use nominal pipe size or inside diameter?
Use the actual internal flow diameter. Nominal pipe size and outside diameter can differ significantly from the internal bore, especially across schedules and wall thicknesses.
Can I use this page when I only know volume collected over time?
Not directly. If you know a collected volume and elapsed time, compute volumetric flow rate from Q = V/t. This calculator is specifically for area-velocity and circular-pipe-diameter relationships based on Q = A v.
Why does this page ask for average velocity instead of peak velocity?
Because volumetric flow rate is related to the average bulk velocity across the full section. Real velocity profiles are not perfectly flat, so a local centerline velocity can be higher than the average value used in Q = A v.