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.
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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*\rho*v^2
To solve for density:
\rho = q/(0.5*v^2)
To solve for speed:
v = sqrt(q/(0.5*\rho)) = sqrt(2*q/\rho)
- q = dynamic pressure, also called velocity pressure
- ρ = fluid density
- v = fluid or object speed relative to the fluid
If you leave dynamic pressure blank, the calculator uses density and speed to calculate q. If you leave density blank, it rearranges the formula to calculate ρ. If you leave speed blank, it rearranges the formula to calculate v. Unit conversions are applied before the formula is evaluated, then the result is converted back to the unit you selected.
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*30^2
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?
This formula is commonly used for incompressible flow or low-speed gas flow where density changes are small. For high-speed compressible flow, especially when air speed approaches a significant fraction of the speed of sound, compressibility effects may need to be considered.