Pressure–Head Converter

Convert a pressure difference to equivalent fluid head, or fluid head to pressure difference, using an explicit fluid density and gravitational acceleration. Choose SI or engineering units and inspect the normalized values and calculation steps.

Formula and method

Pressure head is pressure per unit weight of fluid. With constant mass density ρ and gravitational acceleration g:

H = Δp / (ρg) and Δp = ρgH. The specific weight is γ = ρg.

The engine normalizes pressure to Pa, head to m, mass density to kg/m³, and gravity to m/s². It calculates γ in N/m³, then converts the requested output unit. Dimensionally, Pa / (N/m³) = m. Imperial inputs are normalized to SI before calculating, so no separate numerical g_c factor is needed.

Pressure reference, sign, and fluid basis

• Use a consistent pressure reference. Define Δp = p₂ − p₁ using two absolute pressures or two gauge pressures with the same reference. A single gauge pressure can represent the difference from that gauge’s reference. No atmospheric pressure is added or subtracted.
• Signed values are preserved. Positive, negative, and zero pressure differences produce positive, negative, and zero equivalent head. Reversing the pressure difference reverses the head sign. This is not a sign convention for frictional head loss or pump head.
• Head is a length of the supplied fluid. A result in m or ft does not imply water. Enter mass density at the relevant temperature, pressure, and composition; lbm/ft³ means mass per volume, not lbf/ft³ specific weight. No fluid-property lookup or assumed water density is applied.
• Gravity is explicit. The initial 9.80665 m/s² is standard gravity, a conventional reference value. Replace it when a different known local acceleration is appropriate. Density and gravity must both be positive.

Assumptions and validity

• The calculation uses one constant, representative density and one constant gravity. For a static column, the depth corresponding to a pressure increase obeys Δp = ρgH. A fluid with substantial density variation requires integration of the hydrostatic relation.
• For flowing fluid, the result is the pressure-head component. Elevation head, velocity head, friction losses, pump total head, hydraulic power, and NPSH require their own inputs and energy balance.
• m and ft are head lengths for the supplied fluid. Fixed pressure units such as mmH₂O or inH₂O have reference-fluid conventions and are not offered as head-length choices here. The atm pressure unit means 101325 Pa and does not specify the local atmosphere.
• Arithmetic uses double precision. Results display up to 8 significant digits and calculation steps up to 10. All normalized inputs, specific weight, pressure, head, and output must be finite and representable; nonzero underflow is rejected. Unit and range checks do not establish equipment suitability.

Worked examples

Pressure to head: given Δp = 98.0665 kPa, a supplied density of 1000 kg/m³, and g = 9.80665 m/s², first convert Δp = 98066.5 Pa. Then γ = 1000 × 9.80665 = 9806.65 N/m³ and H = 98066.5 / 9806.65 = 10 m. The example density is illustrative; it is not a water-property prediction.

Head to pressure: using H = 10 m with the same density and gravity gives Δp = 9806.65 × 10 = 98066.5 Pa = 98.0665 kPa. At 800 kg/m³, that same 10 m head produces 78.4532 kPa; the original 98.0665 kPa corresponds to 12.5 m of that less dense fluid.

Imperial basis: 100 psi with ρ = 62.4 lbm/ft³ at standard gravity corresponds to approximately 230.76923 ft of that fluid. Load the example and change units to check equivalent inputs; changing direction carries the last valid converted value into the new input.

For pressure-to-pressure scale conversions without a fluid-density calculation, use the Engineering Unit Converter.

Sources and calculation version

• OpenStax, College Physics 2e, section 11.4: Variation of Pressure with Depth in a Fluid — the constant-density hydrostatic pressure relation and its limits.
• NIST SP 811, Appendix B.9 — pressure, length, mass-density, acceleration conversions, and standard gravity. International feet/inches and avoirdupois mass units are used.

Changelog: engine 1.0.0 introduces bidirectional pressure/head conversion, explicit density and gravity, signed and zero results, SI intermediates, unit conversion, worked steps, and numerical-range checks. Factor registry 1.0.0 is shared with the Engineering Unit Converter. Parameter source: your density and gravity; no material-property dataset is used. Engineering review status: independent review pending.