Flow Rate Calculator

How to use the Flow Rate Calculator

What this calculator does

This calculator estimates the volumetric flow rate of a fluid from cross-sectional area and average velocity, and it can also estimate mass flow when density is supplied. It supports a circular pipe, a rectangular duct, or a directly entered cross-sectional area. The governing relationship is the velocity-area identity Q = A × v; mass flow is ṁ = ρ × Q. These equations describe steady average flow through a section. They do not predict pressure loss, pump power, turbulence, compressibility effects, or the velocity profile inside the passage. For those questions, a fuller fluid-system model is required. The velocity-area flow principle gives useful background on relating mean velocity and area to discharge.

When to use it

Use the calculator to estimate water delivery through a pipe, air movement through a rectangular duct, process-fluid throughput when the internal area is known, or mass flow when a fluid density is available. It is also useful for quick unit conversions because the same canonical result can be displayed in SI or common U.S. customary flow units.

How to calculate

1. The calculator opens with a ready-to-use demonstration: a 3 in circular pipe, 10 ft/s average velocity, and water-like density of 998 kg/m³. The example results and a validated XLSX workbook are available immediately.
2. Choose Shape. For a pipe, keep Circular pipe and enter Diameter. For a duct, choose Rectangular duct and enter Width and Height. If geometry is irregular or area is already known, choose Known area and enter Cross-sectional area.
3. Set Length unit or Area unit to match the geometry data. Changing a dimensional input unit converts the current value rather than merely relabeling it.
4. Enter the required Velocity and choose Velocity unit. The value is the average velocity across the section, not necessarily a local centerline or point velocity.
5. Optionally enter Density and choose Density unit. Leave Density blank if only volumetric flow is needed; mass-flow outputs will then be shown as unavailable.
6. Choose Volumetric flow unit and Mass flow unit for the headline display, then read the result cards and the SI detail table. Select Download Excel to export the current canonical inputs and outputs. Reset clears the demonstration and all numeric inputs; after Reset, Download Excel is disabled until enough valid data is entered again.

Input guide

Shape is a required categorical control: Circular pipe, Rectangular duct, or Known area. It determines which area equation is used. Diameter is required only for Circular pipe; enter a positive decimal such as 3 with Length unit set to in. Larger diameter increases area with the square of diameter, so flow rises quickly when velocity is fixed. Do not enter an outside diameter when the fluid actually occupies a smaller internal bore. For Rectangular duct, Width and Height are both required positive decimals; an example is 0.20 m by 0.10 m. Their product defines area, so doubling either dimension doubles flow at fixed velocity. Length unit applies to Diameter, Width, and Height and accepts m, cm, mm, in, or ft.

Cross-sectional area is required only for Known area; use a positive decimal such as 0.015 with Area unit m², cm², mm², in², or ft². A common mistake is entering a diameter or radius where an area is expected. Velocity is required and accepts a nonnegative decimal such as 10; its unit can be m/s, ft/s, cm/s, or km/h. Zero velocity is valid and produces zero volumetric flow. Negative velocity is rejected because this calculator reports flow magnitude rather than signed direction. Density is optional and must be positive if entered; 998 kg/m³ is a realistic water example near room temperature. Density may be entered in kg/m³ or lb/ft³. Higher density does not change volumetric flow, but it increases mass flow in direct proportion. For real fluids, density can vary with temperature and pressure, so use a value appropriate to the operating condition.

Volumetric flow unit selects m³/s, ft³/s, L/s, L/min, or US gal/min for the primary result. It changes presentation only. Mass flow unit similarly selects kg/s, lb/s, kg/min, or lb/min for mass flow. These output-unit controls never alter the canonical calculation. The NIST flow-unit conversion factors provide authoritative reference values for common volume-per-time conversions.

Output guide

Volumetric flow rate is the primary output: the volume crossing the section per unit time, displayed in your selected Volumetric flow unit. It is exactly proportional to both cross-sectional area and average velocity. A zero result means velocity is zero; a larger result means more volume passes per unit time. Mass flow rate is an estimate of mass per unit time and appears only when Density is supplied. It scales with area, velocity, and density. Cross-sectional area is the geometry-derived area in m², and Volumetric flow, SI shows the same Q in m³/s. Mass flow, SI shows ṁ in kg/s when density is present. The four summary pills report the active shape, area, entered velocity, and density so that the result can be checked against the assumptions at a glance.

The Result details table repeats the canonical SI state used for both display and export. Its columns are Quantity, Value, Unit, and Meaning. Cross-sectional area, Average velocity, Volumetric flow rate, and Mass flow rate are model values, not independently rounded calculations. A missing mass-flow row means Density was left blank. Because the table uses SI values, it remains stable when only a headline output unit is changed.

Worked example

The startup example uses a circular pipe with Diameter = 3 in, Velocity = 10 ft/s, and Density = 998 kg/m³. Converting the diameter gives 0.0762 m, so the circular area is π × (0.0762 ÷ 2)² = 0.004560367 m². Converting 10 ft/s gives 3.048 m/s. Therefore Q = A × v = 0.004560367 × 3.048 = 0.0138999996 m³/s, which is displayed as 0.4909 ft³/s. Multiplying by density gives 13.8721996 kg/s, displayed as 30.58 lb/s. These are the first-open results and the same canonical values are written to the downloadable workbook.

Learn more

For unit-system conventions and derived quantities, see the NIST guidance on SI base and derived units. For pipe-specific checks, the pipe velocity relation shows the same velocity-area relationship rearranged to solve for velocity from diameter and flow.