What is flow rate?

Flow rate tells you how fast fluid or bulk material moves through a cross-section. Engineers use two flavors. Volume flow Q reports how many cubic units pass per time. Mass flow ṁ reports total mass per time.

The two are linked by density. If you know volume flow and density, you can find mass flow immediately.

• Volume flow: Q = A × v
• Mass flow: ṁ = ρ × Q

Here A is cross-sectional area, v is average fluid velocity, and ρ is density. That’s the whole story in two tidy equations.

How the calculator works

You pick a shape, enter its dimensions, add the fluid velocity, then choose density if you want mass flow. The calculator converts everything to SI behind the scenes to keep precision tight. It then converts results to your chosen output units.

Behind the scenes in one glance

• Compute A from the selected shape.
• Multiply by v to get volume flow Q.
• Multiply Q by ρ for mass flow ṁ.
• Convert results to user-selected units without rounding drift.

You can use inches, feet, yards, millimeters, centimeters, or meters for dimensions. Choose feet per second, feet per minute, miles per hour, or meters per second for velocity. Density options include lb/ft³, lb/yd³, lb/in³, kg/m³, kg/L, g/L, and g/cm³.

Units and conversions (quick table)

When you’re in the field, you want clean conversions at a glance. Use the table below as a pocket guide. The calculator performs these conversions automatically in the background.

Pipe shapes & area formulas

Area changes everything. The same velocity through a larger area yields a higher flow rate. The calculator covers four scenarios.

1) Circular pipe (full)

A = π(d/2)²

Measure the inside diameter. Schedule 40, 80, and other pipe schedules share nominal sizes but not the same inside diameter. Check the spec sheet if accuracy matters.

2) Circular pipe (partially filled)

A = R²·acos((R − h)/R) − (R − h)·√(2Rh − h²) with R = d/2

This is the classic circular segment area. It handles storm drains, gravity sewers, and channels where the liquid doesn’t fill the pipe.

3) Rectangular channel

A = w × h

Use clear internal width and the depth of the flowing layer. If the channel has rounded fillets, reduce effective width a bit.

4) Other shapes (custom area)

Sometimes geometry is messy. You can compute area elsewhere and drop the value in directly. The calculator accepts in², ft², yd², cm², or m².

Step-by-step examples

Example A — Schedule 40 pipe at moderate speed

Suppose you have a 3-inch inside diameter pipe conveying water at 6 ft/s. Density is roughly 62.4 lb/ft³.

1. Area: A = π(3 in ÷ 2)² = π(1.5 in)² = 7.069 in² → 0.0491 ft².
2. Volume flow: Q = A × v = 0.0491 ft² × 6 ft/s = 0.2946 ft³/s ≈ 132.1 US gal/min.
3. Mass flow: ṁ = ρ × Q = 62.4 lb/ft³ × 0.2946 ft³/s = 18.4 lb/s.

That one number answers a lot. You can check pump curves, nozzle sizes, and pressure drops with confidence.

Example B — Partially full culvert

A 36-inch culvert runs at a 12-inch liquid depth during a storm. The average velocity is 4 ft/s.

1. Radius R = 18 in, depth h = 12 in.
2. Segment area via the formula above → about 350.1 in² → 2.431 ft².
3. Flow: Q = 2.431 × 4 = 9.724 ft³/s ≈ 435.6 US gal/min.

You can repeat this for any depth. Just stay within the realistic range 0 ≤ h ≤ d.

Example C — Rectangular channel with slurry

A channel 2 ft wide carries a mineral slurry 10 inches deep. Average velocity is 3 ft/s. Density is 95 lb/ft³.

1. Area: A = 2 ft × 10 in = 2 × 0.8333 ft = 1.6667 ft².
2. Volume flow: Q = 1.6667 × 3 = 5.000 ft³/s.
3. Mass flow: ṁ = 95 × 5 = 475 lb/s.

Mass flow matters here because heat load, reaction rates, and wear all scale with mass.

Choosing the correct units

Match your result units to the downstream task. If you’re reading a pump curve in US gallons per minute, show Q in GPM. If you’re calculating residence time in a reactor, show Q in m³/s or L/min for clean arithmetic.

• Plant operations: ft³/s and lb/s often align with control system tags.
• Water/wastewater: MGD, GPM, and ft³/s dominate daily reports.
• HVAC: CFM for air volume, then lb/s or kg/s for heat balance.
• Process design: m³/s and kg/s tie into energy and mass balance directly.

Common pitfalls & how to avoid them

Using outside diameter

Outside diameter overstates area. Most commercial pipe tables list both OD and wall thickness. Subtract twice the wall thickness to get the inside diameter.

Mixing peak velocity with mean velocity

Turbulent flows have flatter profiles but still peak at the center. Instruments often report mean velocity by design. If you used a single-point reading, correct it or take more readings across the section.

Ignoring temperature effects on density

Density changes with temperature and composition. For water the swing is small, yet for hydrocarbons and slurries it’s not trivial. Use the best value you can get from a datasheet or a reputable handbook.

Unit mismatch

If Q looks unrealistic, check units first. Conversions slip when field logs mix inches with feet or minutes with seconds.

Industry use cases

Water & wastewater

Sizing clarifiers, verifying pump capacity, and estimating storm inflows rely on quick flow checks. With partial pipes the segment formula is worth its weight in gold.

Energy & power

Cooling loops live and die by flow. Mass flow feeds heat balance directly. You’ll translate flow to temperature rise and then to heat rejected by a cooler.

Food & beverage

Recipe integrity depends on dosing. Knowing exact mass flow into a blender lets you keep texture consistent batch to batch.

Mining & minerals

Slurry pipelines need the right velocity window. Too slow and solids settle. Too fast and you burn through the line. Flow rate tells you where you stand.

HVAC & building systems

Whether you’re moving chilled water or outdoor air, flow rate determines capacity. Convert to the units your balancing report expects and you’ll finish faster.

Flow Rate Calculator FAQ

How do I measure velocity if I don’t have a flowmeter?

Use a pitot tube, a small ultrasonic sensor, or a timed float for open channels. For quick checks, timed bucket tests work when flow is low and safe to capture.

What density should I use for air or water?

Many plants use 62.4 lb/ft³ for water and roughly 0.075 lb/ft³ for dry air at standard conditions. If your process runs hot or at altitude, adjust accordingly using a reliable handbook or a datasheet.

Does pipe roughness affect flow rate?

Roughness doesn’t change the definition of Q, yet it affects the velocity you can achieve for a given pressure drop. For pressure-drop estimates, use Darcy–Weisbach or Hazen–Williams methods once you know the flow.

Can I enter a nonstandard shape?

Yes. Choose “Other,” compute the area however you prefer, then enter it with your chosen area unit.

When should I use mass flow instead of volume flow?

Use mass flow when you need heat duty, chemical reactions, or material balances. Use volume flow when you’re focused on container fill time, pump curves, or level rise.

Glossary

• Volume flow (Q): Volume per time passing through a cross-section.
• Mass flow (ṁ): Mass per time passing through a cross-section.
• Velocity (v): Average speed of the fluid along the pipe or channel.
• Density (ρ): Mass per volume. Depends on temperature and composition.
• Cross-sectional area (A): Area of the slice the fluid passes through.

Why this Flow Rate Calculator stands out

• Shape-aware inputs: Circular, partial circular, rectangular, or custom area.
• US-friendly defaults: Inches, ft/s, and lb/ft³ out of the box.
• Clean separation: Inputs on one side, read-only results on the other.
• Fast unit switching: Convert outputs to ft³/s, GPM, L/s, or m³/s instantly.
• Professional rounding: Values round after conversion to avoid drift.

You get the number you need without fuss. That’s the whole point.

Quick cheat cards

Rule-of-thumb velocities

• Water in distribution mains: roughly 3–7 ft/s for noise control.
• Slurry pipelines: keep velocity high enough to prevent settling.
• Air ducts: comfortable ranges vary by application and noise limits.

When your reading looks wrong

• Check whether you entered outside diameter by mistake.
• Verify that the velocity is an average, not a point peak.
• Confirm density units if you need mass flow.
• Scan the output unit. ft³/s and ft³/min differ by a factor of 60.

What is the formula for flow rate?

The core formula is refreshingly short. Volume flow equals cross-sectional area times average velocity: Q = A × v. Mass flow equals density times volume flow: ṁ = ρ × Q. That pair covers most day-to-day engineering calculations from plant utilities to open channels.

Flow numbers drive decisions across plants, buildings, and infrastructure. With this Flow Rate Calculator you can move from sketch to number in seconds, then switch units to match whatever report or spec you’re working on. Keep a few rules of thumb in your back pocket, measure carefully, and you’ll make solid calls every time.

Try the calculator now, then bookmark it for the next job. When you need fast, trustworthy results, our Flow Rate Calculator delivers without drama.