Physics calculators

Flow Rate Calculator

Updated May 20, 2026 By Jehan Wadia
Solve For
Cross-Section Shape
Enter a positive diameter
Flow Parameters
Enter a positive velocity
Enter a positive flow rate

Results — Continuity Equation (Q = A × v)
Cross-Sectional Area
0.007854 m²
Velocity
2.0000 m/s
Volumetric Flow Rate
0.015708 m³/s
Flow Rate (converted)
15.708 L/s
Unit Conversions
m³/s0.015708
L/s15.708
L/min942.48
GPM (US)248.98
CFM33.28
ft³/s0.5548
Solve For
Cross-Section Shape
Flow & Fluid Parameters
Water ≈ 998 kg/m³, Air ≈ 1.225 kg/m³

Results — Mass Flow Rate (ṁ = ρ × A × v)
Area
0.007854 m²
Velocity
2.0000 m/s
Vol. Flow Rate (Q)
0.01571 m³/s
Density (ρ)
998 kg/m³
Mass Flow Rate (ṁ)
15.68 kg/s
Flow Rate Conversions
m³/s
L/s
L/min
GPM (US)
kg/s
lb/s
Hazen-Williams Pipe Flow
Calculate volumetric flow rate in pressurized closed conduits using Q = 0.2785 × C × d2.63 × S0.54, where S = head loss / length.
Enter a valid C-factor (1–200)
Enter a positive diameter
Enter a positive length
Expressed as head of water or pressure units.
Enter a positive head loss

Results — Hazen-Williams
Volumetric Flow Rate
Flow Velocity
Hydraulic Gradient (S)
Reynolds Number (est.)
Flow Rate Conversions
m³/s
L/s
L/min
GPM (US)
CFM

Introduction

Flow rate tells you how much fluid moves through a pipe or channel over a set amount of time. It is one of the most important values in fluid mechanics, used in plumbing, water supply, HVAC systems, and chemical processing. This Flow Rate Calculator helps you find volumetric flow rate, mass flow rate, or pipe velocity quickly and accurately.

The tool has three modes. The Continuity Equation mode uses the formula Q = A × v, where Q is the volumetric flow rate, A is the cross-sectional area, and v is the fluid velocity. You can solve for any one of these three values. The Mass Flow Rate mode adds fluid density to the equation, using ṁ = ρ × A × v, so you can find how much mass passes through a pipe each second. The Hazen-Williams mode is built for pressurized water pipes and calculates flow rate based on pipe diameter, length, head loss, and a roughness coefficient.

You can choose from several pipe cross-section shapes, including circles, rectangles, ellipses, annular rings, and trapezoids. Every input supports multiple units, and the results section shows your answer converted into common units like liters per second, gallons per minute, and cubic feet per second. Enter your values, hit Calculate, and get your results instantly.

How to use our Flow Rate Calculator

Enter your pipe dimensions, fluid properties, and known flow values to calculate flow rate, velocity, area, or mass flow rate. The calculator has three modes, and results include unit conversions and a visual chart.

Mode Selection (Tabs): Pick one of three calculation methods — Continuity Equation (Q = A × v) for basic volumetric flow, Mass Flow Rate (ṁ = ρ × A × v) when fluid density matters, or Hazen-Williams for estimating flow in pressurized water pipes based on pipe material and head loss.

Solve For: In the Continuity and Mass Flow Rate modes, choose which value you want the calculator to find. Options include flow rate, velocity, pipe area or dimensions, and (in Mass Flow Rate mode) density or mass flow rate. The field you solve for will lock automatically.

Cross-Section Shape: Select the shape of your pipe or channel. Choose from circle, rectangle, ellipse, annulus (pipe within a pipe), trapezoid, or enter a known area directly. The input fields will change to match the shape you pick. If you need help computing a specific cross-sectional geometry, tools like our Circle Area Calculator, Area of a Rectangle Calculator, or Trapezoid Area Calculator can be useful references.

Pipe Dimensions: Enter the size of your pipe or channel in the fields that appear for your chosen shape. For a circle, enter the diameter. For a rectangle, enter width and height. Use the dropdown next to each field to pick your preferred unit (meters, centimeters, millimeters, inches, or feet).

Velocity (v): Enter the speed of the fluid moving through the pipe. You can use meters per second, feet per second, kilometers per hour, or miles per hour. For general motion calculations, you may also find our Speed Calculator helpful.

Flow Rate (Q): Enter or view the volumetric flow rate. Available units include cubic meters per second, liters per second, liters per minute, gallons per minute (GPM), cubic feet per minute (CFM), and cubic feet per second.

Density (ρ) — Mass Flow Rate mode only: Enter the density of your fluid. Water is about 998 kg/m³ and air is about 1.225 kg/m³. You can enter values in kg/m³, lb/ft³, or g/cm³. If you need to determine the density of a material first, try our Density Calculator.

Mass Flow Rate (ṁ) — Mass Flow Rate mode only: Enter or view the mass flow rate in kg/s, kg/min, lb/s, or lb/min. This tells you how much mass passes through the pipe each unit of time.

C-Factor — Hazen-Williams mode only: Select the pipe material from the dropdown to set the roughness coefficient. Common values include 150 for PVC, 130 for new cast iron, and 100 for old cast iron. You can also enter a custom value.

Pipe Length — Hazen-Williams mode only: Enter the total length of the pipe run in meters, feet, kilometers, or miles.

Head Loss — Hazen-Williams mode only: Enter the pressure drop along the pipe. You can use meters of water, feet of water, psi, kPa, or bar. For related pressure calculations in static fluid columns, see our Hydrostatic Pressure Calculator.

Calculate / Reset: Press the "Calculate" button to see your results, or press "Reset" to return all fields to their default values. You can also press Enter on your keyboard while in any input field to run the calculation.

What Is Flow Rate?

Flow rate is the amount of fluid (liquid or gas) that moves through a pipe, channel, or opening in a given amount of time. Think of it like measuring how much water comes out of a garden hose every second. Engineers, plumbers, and scientists use flow rate to design water systems, ventilation ducts, irrigation setups, and much more.

There are two main types of flow rate. Volumetric flow rate measures the volume of fluid passing a point per unit of time — for example, liters per second or gallons per minute. Mass flow rate measures the mass of fluid passing per unit of time, such as kilograms per second. Mass flow rate matters most when the fluid's density can change, like with gases that compress or expand.

Key Equations Used in Flow Rate Calculations

The Continuity Equation: Q = A × v

This is the most basic flow rate formula. It says that the volumetric flow rate (Q) equals the cross-sectional area of the pipe (A) multiplied by the fluid velocity (v). If you know any two of these three values, you can solve for the third. For example, if water flows at 2 meters per second through a pipe with a diameter of 10 centimeters, you can quickly find how many liters per second are moving through that pipe.

The cross-sectional area depends on the shape of the pipe or channel. A round pipe uses the circle area formula (π × r²). But pipes and ducts can also be rectangular, elliptical, annular (a pipe inside a pipe), or trapezoidal, which is common in open channels. For more detail on calculating internal pipe volumes, see our Pipe Volume Calculator.

Mass Flow Rate: ṁ = ρ × A × v

The mass flow rate formula adds one more variable: density (ρ). It tells you how many kilograms of fluid flow past a point each second. This equation is especially important when working with air, steam, or any gas, because gas density changes with temperature and pressure. For water at room temperature, density is about 998 kg/m³. For air, it is only about 1.225 kg/m³ — roughly 800 times less dense. If you're working with gases and need to relate pressure, volume, and temperature, our Ideal Gas Law Calculator can help determine the fluid's state.

The Hazen-Williams Equation

The Hazen-Williams formula is a widely used equation for estimating flow rate in pressurized water pipes. It accounts for pipe diameter, pipe length, the head loss (pressure drop) along the pipe, and the roughness of the pipe's inner surface. The roughness is represented by a C-factor. Smooth plastic pipes have a high C-factor (around 150), while old, corroded steel pipes have a low C-factor (around 80). A higher C-factor means less friction and more flow for the same pressure drop.

This equation is used mainly for water at normal temperatures. It is not meant for very viscous fluids or gases. Engineers rely on it for designing municipal water systems, fire sprinkler lines, and irrigation networks because it gives fast, practical results without complex friction factor calculations. For a more detailed pipe analysis that includes friction factors and the Darcy-Weisbach equation, you can use our Pipe Flow Calculator.

Common Flow Rate Units

Flow rate can be expressed in many units depending on the industry and country. The most common ones include:

  • m³/s — cubic meters per second (SI standard)
  • L/s and L/min — liters per second or per minute
  • GPM — gallons per minute (common in the United States)
  • CFM — cubic feet per minute (common for air and HVAC systems; see also our CFM Calculator for ventilation sizing)
  • kg/s — kilograms per second (for mass flow rate)

Why Flow Rate Matters

Getting the flow rate right is critical in many real-world situations. A plumber needs to know if a pipe is big enough to supply water to a building. An engineer designing a cooling system needs to make sure enough coolant moves through the equipment every minute. A firefighter depends on pumps that deliver the right number of gallons per minute. In all these cases, understanding the relationship between pipe size, fluid speed, and flow rate helps people choose the right pipe diameter, pump size, and system layout.

Flow rate is also closely connected to other fluid mechanics concepts. Knowing whether a flow is laminar or turbulent — determined by the Reynolds Number Calculator — affects friction losses and system efficiency. The Viscosity Calculator helps quantify a fluid's internal resistance to flow, while the Buoyancy Calculator is useful when analyzing objects submerged in flowing fluids. For systems where fluid forces are a concern, tools like the Force Calculator and Kinetic Energy Calculator can round out your analysis by relating flow conditions to the forces and energy within the system.


Frequently asked questions

What is the difference between volumetric flow rate and mass flow rate?

Volumetric flow rate (Q) measures the volume of fluid passing a point per unit of time, like liters per second. Mass flow rate (ṁ) measures the mass of fluid passing per unit of time, like kilograms per second. They are related by density: ṁ = ρ × Q. Use mass flow rate when the fluid can be compressed, like air or steam.

How do I find the cross-sectional area of a round pipe?

Use the circle area formula: A = π × (d/2)². Just enter the pipe's inner diameter into the calculator, select the "Circle" shape, and the tool computes the area for you automatically.

What is the C-factor in the Hazen-Williams equation?

The C-factor is a number that represents how smooth or rough the inside of a pipe is. A higher C-factor means a smoother pipe with less friction. PVC pipes have a C-factor of about 150. Old corroded steel pipes may have a C-factor as low as 80. Smoother pipes allow more water to flow for the same pressure drop.

Can I use this calculator for gases like air?

Yes, but only with the Continuity Equation and Mass Flow Rate modes. The Hazen-Williams mode is designed only for water in pressurized pipes. For gases, make sure to enter the correct density. Air at room temperature has a density of about 1.225 kg/m³.

What does head loss mean?

Head loss is the drop in pressure that happens as water flows through a pipe due to friction. It is often measured in meters of water or feet of water. Longer pipes, smaller diameters, and rougher surfaces all cause more head loss. The Hazen-Williams mode uses head loss to estimate flow rate.

How do I convert GPM to liters per minute?

Multiply gallons per minute (GPM) by 3.785 to get liters per minute. For example, 10 GPM = 37.85 L/min. This calculator shows all common conversions in the results section automatically.

What pipe shape should I choose for a standard round pipe?

Select Circle from the cross-section shape dropdown. Then enter the pipe's inner diameter. This is the most common shape for plumbing, water supply, and gas pipes.

Why is my result field locked and grayed out?

The locked field is the value the calculator will solve for. When you pick "Solve For" a certain variable, that field becomes read-only so you can enter the other known values. The calculator fills in the locked field after you press Calculate.

What is an annulus cross-section?

An annulus is a ring shape formed when a smaller pipe sits inside a larger pipe. The flow area is the space between the two pipes. Enter the outer diameter and inner diameter, and the calculator finds the ring-shaped area: A = π × ((D_outer/2)² − (D_inner/2)²).

Does pipe diameter really matter that much for flow rate?

Yes, diameter has a huge effect. In the continuity equation, area depends on the square of the diameter. In the Hazen-Williams equation, flow rate depends on diameter raised to the power of 2.63. Doubling the diameter can increase flow rate by more than six times.

What units should I use for velocity?

Use whichever unit you are comfortable with. The calculator accepts meters per second (m/s), feet per second (ft/s), kilometers per hour (km/h), and miles per hour (mph). It converts everything internally to m/s for the calculation.

What density should I use for water?

At room temperature (about 20°C or 68°F), water has a density of roughly 998 kg/m³. This is the default value in the Mass Flow Rate mode. If the water is much hotter or colder, the density will change slightly.

Can I use the Hazen-Williams mode for oil or other fluids?

No. The Hazen-Williams equation was created specifically for water flowing in pressurized pipes at normal temperatures. It does not work well for oil, chemicals, or very viscous fluids. For those, use the Continuity Equation or Mass Flow Rate modes instead.

What is the hydraulic gradient shown in the Hazen-Williams results?

The hydraulic gradient (S) is the head loss divided by the pipe length. It tells you how much pressure is lost per unit of pipe length. A value of 0.1 m/m means the water loses 0.1 meters of head for every 1 meter of pipe.

How do I calculate flow rate if I only know the pipe size and pressure?

Use the Hazen-Williams mode. Enter the pipe diameter, pipe length, head loss (pressure drop), and select the pipe material for the C-factor. The calculator will find the volumetric flow rate and velocity for you.

What does the Reynolds number in the Hazen-Williams results mean?

The Reynolds number is an estimate that tells you if the flow is smooth (laminar) or chaotic (turbulent). Values below about 2,300 indicate laminar flow. Values above 4,000 indicate turbulent flow. Most pipe flows in practice are turbulent.

Can I enter pipe dimensions in inches and get results in metric?

Yes. Each input field has a unit dropdown. You can enter dimensions in inches, feet, or any supported unit. The results always show values in SI units (m², m/s, m³/s) and also provide conversions to other common units.

What is the Direct Area Input option for?

If you already know the exact cross-sectional area of your pipe or channel, select Direct Area Input from the shape dropdown. Then type in the area value directly instead of entering individual dimensions like diameter or width.