Calculate dynamic pressure, density, or speed from any two values using q = 0.5ρv² and units in Pa, psi, bar, atm, kg/m³, m/s, mph, ft/s.

Relate dynamic (velocity) pressure, density and speed. Dynamic pressure is not static or supply pressure.

Use density at the conditions of the flow.

Dynamic Pressure Formula

The dynamic pressure formula relates velocity pressure, fluid density, and speed. The calculator uses SI base units internally: pascals for pressure, kilograms per cubic meter for density, and meters per second for speed.

q = 0.5 × ρ × v²

To solve for density:

ρ = q / (0.5 × v²)

To solve for speed:

v = sqrt(q / (0.5 × ρ)) = sqrt(2 × q / ρ)
  • q = dynamic pressure, also called velocity pressure
  • ρ = fluid density
  • v = fluid or object speed relative to the fluid

Select the value to solve for, enter the other two quantities and select Calculate. Input units are converted before calculation. The primary answer uses SI units, with the other original units shown below it.

Common Density Values and Unit Conversions

Use these values as rough references when you need a density input. Actual density changes with temperature, pressure, humidity, and fluid composition.

Fluid or condition Typical density Notes
Air at sea level, about 15°C 1.225 kg/m³ Common reference value for aerodynamics
Air at room temperature, about 20°C 1.204 kg/m³ Often used for HVAC and indoor air estimates
Water, about 20°C 998 kg/m³ Much denser than air, so dynamic pressure rises quickly
Seawater 1025 kg/m³ Approximate value, varies with salinity and temperature
Quantity Conversion
Pressure 1 psi = 6894.76 Pa
Pressure 1 bar = 100,000 Pa
Pressure 1 atm = 101,325 Pa
Density 1 lb/ft³ = 16.0185 kg/m³
Speed 1 mph = 0.44704 m/s
Speed 1 ft/s = 0.3048 m/s

Examples

Example 1: Calculate dynamic pressure from air speed

Suppose air density is 1.225 kg/m³ and speed is 30 m/s.

q = 0.5 × 1.225 × 30²
q = 551.25 Pa

The dynamic pressure is 551.25 Pa.

Example 2: Calculate speed from dynamic pressure

Suppose dynamic pressure is 1000 Pa and air density is 1.225 kg/m³.

v = sqrt(2 × 1000 / 1.225)
v = 40.41 m / s

The speed is about 40.41 m/s.

FAQ

What is dynamic pressure?

Dynamic pressure is the pressure associated with the motion of a fluid. It represents the kinetic energy per unit volume of the moving fluid. For a given density, dynamic pressure increases with the square of speed, so doubling speed makes dynamic pressure four times larger.

Is dynamic pressure the same as static pressure?

No. Static pressure is the pressure a fluid exerts when measured with no effect from its motion. Dynamic pressure comes from motion. In fluid flow problems, total pressure is commonly treated as the sum of static pressure and dynamic pressure under suitable conditions.

When is the formula q = 0.5*ρ*v² appropriate?

The formula defines dynamic pressure using local density and speed. Equating it to measured total pressure minus static pressure requires suitable incompressible-flow conditions. Compressible impact-pressure corrections are not included.