Dynamic Pressure Calculator
Pressure carried by a moving fluid, the kinetic energy per unit volume: q = ½ · ρ · V².
Inputs
Enter the fluid density and the flow speed. Air at sea level is about 1.225 kg/m³ and fresh water about 998 kg/m³. Drag the handle (or focus it and press ↑/↓) to reorder. Scientific notation such as 1.2e3 is accepted, and any unit converts automatically.
Results
Enter values and press Calculate. Your answer will appear here.
Dynamic pressure vs. speed
Because q grows with V², doubling the speed quadruples the pressure, which is a straight line of slope 2 on log-log axes. The solid line is your fluid, the dashed lines are half and double its density, and the dot is your flow.
What is being calculated
Reference values
| Air at sea level (1.225 kg/m³) | Speed in km/h | Dynamic pressure q | q in psi |
|---|
Common fluid densities (approximate)
| Fluid | Density | q at 10 m/s |
|---|
Density falls with altitude and rises as the fluid gets colder or more compressed, so use the density at your conditions.
Unit conversions
| Quantity | Conversion |
|---|---|
| Pressure | 1 kPa = 1,000 Pa · 1 bar = 100,000 Pa · 1 psi = 6,894.76 Pa · 1 atm = 101,325 Pa · 1 mmHg = 133.322 Pa · 1 psf = 47.8803 Pa |
| Velocity | 1 km/h = 0.27778 m/s · 1 mph = 0.44704 m/s · 1 kn = 0.514444 m/s · 1 ft/s = 0.3048 m/s |
| Density | 1 g/cm³ = 1,000 kg/m³ · 1 lb/ft³ = 16.0185 kg/m³ · 1 slug/ft³ = 515.379 kg/m³ |
| Area | 1 cm² = 10⁻⁴ m² · 1 ft² = 0.092903 m² · 1 in² = 6.4516×10⁻⁴ m² |
Formula
- q: dynamic pressure (Pa)
- ρ: fluid density (kg/m³)
- V: flow speed relative to the body (m/s)
Example: Air with ρ = 1.225 kg/m³ moving at V = 100 m/s has q = ½ × 1.225 × 100² = 6,125 Pa, which is 6.125 kPa or about 0.888 psi.
Rearranged: V = √(2q / ρ) and ρ = 2q / V². In low-speed flow Bernoulli's equation says p + q = p₀, so a pitot tube reads q = p₀ − p, where p₀ is the total (stagnation) pressure and p the static pressure. The drag force on a body is D = q · Cd · A. The velocity head is V² / (2g), the height of fluid that would give the same pressure. Dynamic pressure is exact as a definition at any speed, but p + q = p₀ is accurate only for nearly incompressible flow, below about Mach 0.3. At higher speed the compressible total pressure is p₀ = p · (1 + 0.2 M²)^3.5 for air (γ = 1.4), where M = V / a. Advanced mode shows both when you enter the static pressure and the speed of sound.
References
- Wikipedia, Dynamic pressure: definition, units and uses
- NASA Glenn, Dynamic Pressure: q in aerodynamics
- Wikipedia, Bernoulli's principle: why p + q is constant along a streamline
- Wikipedia, Pitot tube: measuring q to find airspeed
How to Use This Tool
- Pick a preset, or enter the fluid density ρ and the flow speed V with their units.
- In Advanced, solve for the speed or the density from a known dynamic pressure.
- In Advanced, add the static pressure, speed of sound, or a reference area and drag coefficient for total pressure, Mach number and drag force.
- Click Calculate.
- Read q in the highlighted result, then check the table and the chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Density, speed and pressure units from SI to imperial, with automatic conversion
- Dynamic pressure in Pa, kPa, bar, psi and more, plus the velocity head
- Solve for speed or density, total pressure, Mach number, compressibility check and drag force (Advanced)
- Log-log pressure-vs-speed chart and a labelled pitot-tube diagram
- Reorderable inputs, presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| q | Dynamic pressure | Pa |
| ρ | Air density | kg/m3 |
| V | Airspeed | m/s |
What it means
Dynamic pressure is a measure of the kinetic energy of the flow per unit volume and is a key parameter in aerodynamics. It appears in the lift and drag equations, and in Bernoulli’s equation as the pressure component associated with velocity. It is used to non‑dimensionalise forces via coefficients (C_L, C_D). In flight instruments, the pitot tube measures total pressure, from which dynamic pressure is derived. Dynamic pressure is also used in structural load calculations and in determining the airspeed of an aircraft (true airspeed from calibrated airspeed). It increases with the square of velocity, meaning that aerodynamic forces grow rapidly with speed. Understanding q is fundamental for aircraft performance and structural design.
Worked example
Dynamic Pressure – Two Examples
Real‑World| Parameter | Value |
|---|---|
| ρ | 1.225 kg/m³ |
| V | 100 m/s |
| Parameter | Value |
|---|---|
| ρ | 0.001 kg/m³ |
| V | 7500 m/s |
Common mistakes
- Dynamic pressure q: q = ½ρV² – in Pa (N/m²).
- Density ρ: Use local air density (altitude dependent).
- Speed V: True airspeed, not indicated airspeed.
- Units: ρ in kg/m³, V in m/s → q in kg/(m·s²) = Pa.
- Loads: Dynamic pressure is used to compute aerodynamic forces (L = q·S·C_L).
Applications
Dynamic pressure, q = ½ρV², is the kinetic energy per unit volume of a fluid in motion. It is a key parameter in aerodynamics, appearing in the lift and drag equations as the multiplying factor. Engineers use dynamic pressure to scale aerodynamic forces from wind tunnel models to full‑scale aircraft, to compute loads on structures, and to assess the severity of gusts. In flight test, dynamic pressure is monitored to ensure structural limits are not exceeded. It also governs the hinge moments on control surfaces, influencing actuator sizing. By understanding dynamic pressure, aerospace engineers can predict aerodynamic forces, design robust structures, and ensure safe operation across the flight envelope.
- Aerodynamic force scaling from wind tunnel models
- Structural load analysis for wings, empennage, and control surfaces
- Gust load and manoeuvre load prediction
- Control surface hinge moment and actuator sizing
- Flight envelope monitoring and limiting
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