Flow Rate Calculator

Flow rate calculator: Q = V × A

This flow rate calculator multiplies water velocity by the pipe’s inside cross-sectional area to get flow: Q = V × A. Area is π × (diameter ÷ 2)², with the diameter converted from inches to feet. The result is shown in gallons per minute (cfs × 448.831), cubic feet per second, and liters per minute (cfs × 1,699.01). With the defaults, 5 ft/s through a 4 inch pipe gives 0.436 cfs, or 195.84 GPM.

Use it when you know, or can estimate, how fast water moves, and you want to know how much arrives.

What the formula means

Picture a slice of water one foot long moving through the pipe. Its volume is the pipe area times one foot. If the water travels 5 feet each second, five of those slices pass any point every second. That is what Q = V × A says.

The unit conversions come from fixed facts: one cubic foot is 7.48052 US gallons, and there are 60 seconds in a minute, so 7.48052 × 60 = 448.831.

Worked examples

1. The default: 5 ft/s in a 4 inch pipe

• Diameter: 4 ÷ 12 = 0.333 ft, radius 0.1667 ft
• Area: 3.1416 × 0.1667² = 0.0873 sq ft
• Flow: 5 × 0.0873 = 0.436 cfs
• GPM: 0.436 × 448.831 = 195.84 GPM
• L/min: 741.3 L/min

2. A 2 inch supply line at 4 ft/s

• Area: 3.1416 × (1 ÷ 12)² = 0.0218 sq ft
• Flow: 4 × 0.0218 = 0.087 cfs, or 39.17 GPM

3. A 6 inch line at 3 ft/s

• Area: 0.1963 sq ft
• Flow: 0.589 cfs, 264.38 GPM, or about 1,000.8 L/min

Flow at 5 ft/s by pipe size

Inside diameter	Area (sq ft)	CFS	GPM
1 in	0.0055	0.027	12.24
2 in	0.0218	0.109	48.96
3 in	0.0491	0.245	110.16
4 in	0.0873	0.436	195.84
6 in	0.1963	0.982	440.64
8 in	0.3491	1.745	783.36

Same flow, different pipe: how velocity changes

Flip the formula around and V = Q ÷ A. If 195.84 GPM must pass through a smaller pipe, the water has to speed up. In a 3 inch pipe the area is 0.0491 sq ft, so velocity rises from 5 ft/s to 0.436 ÷ 0.0491 = 8.9 ft/s. In a 6 inch pipe it slows to 0.436 ÷ 0.1963 = 2.2 ft/s.

A smaller pipe is cheaper to buy, but the faster water loses more pressure to friction and makes more noise. A larger pipe costs more but lets a pump work less hard. Designers pick the size that keeps velocity in a sensible range for the job.

Flow unit conversions

From	To	Multiply by
cfs	GPM	448.831
cfs	L/min	1,699.01
GPM	L/min	3.78541
GPM	cfs	0.002228
cfs	cubic meters per second	0.0283168

How to get good inputs

• Inside diameter: look up the bore for your pipe type and schedule. Schedule 40 and Schedule 80 pipe of the same nominal size have different bores.
• Velocity from a bucket test: if you can time how long a known volume takes to fill, you already have the flow rate. Use the GPM calculator for that, then the pipe velocity calculator to find speed.
• Velocity from a meter: some flow meters read velocity directly. Make sure it reads the average, not the center-line peak.
• Full pipe only: this formula assumes water fills the whole bore.

Common mistakes

• Using nominal size. A “1 inch” pipe may have a bore of about 1.05 in or less depending on type. Small errors in diameter grow when squared.
• Mixing radius and diameter. The box takes diameter. Entering the radius cuts the area, and the flow, to a quarter.
• Assuming high velocity is free. Faster water means more friction loss and noise. Check the pressure drop with the pipe friction loss calculator.
• Using it for open channels. Ditches and partly full drains need the Manning equation calculator.

A planning estimate using standard hydraulics. For code-governed plumbing, fire protection, or drainage design, confirm with a licensed engineer or plumber.