Pressure Gradient Force per Mass

Convert measured three-dimensional Cartesian pressure gradient to signed per-mass acceleration; no Coriolis balance, coordinates or hydrostatic-gravity cancellation inferred.

Description

Pressure-gradient acceleration drives air from higher toward lower pressure.

Pressure-gradient acceleration drives air from higher toward lower pressure. Expressing the gradient per unit distance and dividing by density converts a pressure field into an acceleration vector.^[1]

Convert measured three-dimensional Cartesian pressure gradient to signed per-mass acceleration; no Coriolis balance, coordinates or hydrostatic-gravity cancellation inferred.

When to use Pressure Gradient Force per Mass

Use this tool to convert measured three-dimensional Cartesian pressure gradient to signed per-mass acceleration; no Coriolis balance, coordinates or hydrostatic-gravity cancellation inferred.

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.

How to use Pressure Gradient Force per Mass and understand its results

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
Enter pressureGradientPaPerM, airDensityKgPerM3 using the field table and calculation rules, then run the tool.
Read pressureGradientAccelerationMPerSecond2, pressureGradientAccelerationMagnitudeMPerSecond2. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
pressureGradientPaPerM	Pressure gradient Pa per m	list of number	Required
airDensityKgPerM3	Air density kg per m3	number	Required

Enter exactly three Cartesian pressure-gradient components in Pa/m and a positive air density in kg/m³. The tool negates each component and divides by density, then calculates the vector magnitude. Outputs use m/s² and the same Cartesian axes as the input.

a = −∇p/ρ; magnitude = ||a||

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
pressureGradientAccelerationMPerSecond2	Pressure gradient acceleration m per second2	list of number
pressureGradientAccelerationMagnitudeMPerSecond2	Pressure gradient acceleration magnitude m per second2	number

json

{
  "input": {
    "pressureGradientPaPerM": [
      0.001,
      -0.002,
      0.003
    ],
    "airDensityKgPerM3": 1
  },
  "output": {
    "pressureGradientAccelerationMPerSecond2": [
      -0.001,
      0.002,
      -0.003
    ],
    "pressureGradientAccelerationMagnitudeMPerSecond2": 0.0037416573867739412
  }
}

Limitations and assumptions

This is the pressure-gradient term alone. It does not add gravity, Coriolis acceleration, friction or a hydrostatic correction, and does not integrate a wind trajectory. Confirm whether your gradient includes a vertical component before interpreting that component of the result.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Geostrophic Wind Speed: Compute signed east/north geostrophic vector under caller horizontal pressure gradients, density and Coriolis, not true terrain wind or a pressure-force magnitude alias. For a complementary task, use Frontogenesis Function 2D: Compute 2D adiabatic kinematic material growth of temperature-gradient magnitude from caller local velocity-gradient tensor; no vertical tilting/diabatic term, coordinates or front forecast.

References

Pressure Gradient Force per Mass — tool.io

Similar or alternative tools

Geostrophic Wind Speed
Compute signed east/north geostrophic vector under caller horizontal pressure gradients, density and Coriolis, not true terrain wind or a pressure-force magnitude alias.
Frontogenesis Function 2D
Compute 2D adiabatic kinematic material growth of temperature-gradient magnitude from caller local velocity-gradient tensor; no vertical tilting/diabatic term, coordinates or front forecast.