Bernoulli equation formulas and interpretation
Bernoulli’s equation relates pressure, kinetic, and gravitational potential energy along a streamline.
The migrated calculator preserves its unknown-variable workflow in a lighter responsive layout.
How to use the Bernoulli equation calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
For steady ideal flow, pressure energy, kinetic energy, and elevation energy per volume remain constant along a streamline.
P + ½ρv² + ρgh = constant- P — Pressure
- Static pressure (Pa)
- ρ — Density
- Fluid density (kg/m³)
- v — Velocity
- Flow speed (m/s)
- g — Gravity
- Gravitational acceleration (m/s²)
- h — Elevation
- Height above datum (m)
Level-pipe example
Water accelerates from 2 m/s to 4 m/s at equal elevation.
- Density
- 1000 kg/m³
- Pressure 1
- 100 kPa
- P₂ = P₁ + ½ρ(v₁²-v₂²)
- P₂ = 94 kPa
Result: Downstream pressure is 94 kPa.
Higher velocity corresponds to lower static pressure in this ideal case.
Understanding your results
Interpreting the result
Real systems may require pump, turbine, and head-loss terms.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.