Differential Pressure Calculator

How to use the differential pressure calculator

What this calculator does

This calculator estimates the pressure difference associated with a fluid-flow coefficient relationship, or rearranges the same relationship to estimate volumetric flow rate. Its core model is ΔP = (Q/Kv)² × S, where ΔP is differential pressure in bar under the Kv convention, Q is volumetric flow, Kv is the flow factor expressed on the same flow basis, and S is fluid specific gravity. It is useful for quick valve, restriction, and flow-device checks when a suitable Kv-style coefficient is already known. It does not replace a full pressure-loss analysis for piping networks, fittings, compressible-gas effects, cavitation, viscosity corrections, or manufacturer-specific sizing rules.

Pressure is fundamentally force per unit area. If you need the SI definition or want to confirm bar-to-pascal conversions, the NIST pressure conversion guidance lists 1 bar as 100,000 Pa. For the broader physical connection between fluid speed and pressure, NASA's Bernoulli equation overview provides useful context.

When to use it

• Check the approximate differential pressure across a valve or restriction when Q, Kv, and specific gravity are known.
• Estimate the flow rate consistent with a measured pressure difference and a known flow factor.
• Compare how a denser or lighter liquid changes pressure differential at the same normalized flow ratio.
• Convert one calculated pressure result into bar, kPa, psi, Pa, MPa, or mmHg for reporting or instrument comparison.

How to calculate

1. The calculator opens with a ready-to-use demonstration: Water, specific gravity 1, flow rate 10 L/min, and flow factor 5 L/min. It immediately gives 4.00 bar, and the example XLSX is ready to download.
2. Choose Solve for to select either Differential pressure or Flow rate. The chosen result field becomes calculated while the other quantity is available as an input.
3. Choose the Fluid. A preset fills Specific gravity; choose “Enter a custom specific gravity” to type your own positive value.
4. Enter the active Volumetric flow rate, Flow factor (Kv), or Differential pressure. Use the adjacent unit selectors to match your data. Changing a unit converts the current value rather than only relabeling it.
5. Read the live result cards, then use the Pressure equivalents and Calculation audit tables to verify unit conversions and the normalized ratio. Choose Download Excel to export the current validated state.
6. Reset clears the demonstration and user data, returns mode and unit controls to their neutral defaults, clears calculated output, and disables Download Excel until a complete valid state is entered again.

Input guide

Solve for is a required two-state control: Differential pressure or Flow rate. In Differential pressure mode, Q is entered and ΔP is derived; in Flow rate mode, ΔP is entered and Q is derived. Switch modes when your known and unknown quantities change. A common mistake is to overwrite a calculated field without first switching the mode.

Fluid is a required preset selector. Water uses specific gravity 1.000 in the demonstration. Other presets are approximate engineering values, so use Enter a custom specific gravity when temperature, composition, or your data source requires a different value. Specific gravity is dimensionless, required, and must be greater than 0; 1.00 is a realistic water example. A higher S raises differential pressure proportionally at the same Q/Kv ratio, while in flow-solving mode a higher S lowers the predicted flow for the same pressure difference. Do not enter density units such as kg/m³ in this field.

Volumetric flow rate is a required nonnegative decimal when solving for pressure; the example is 10 L/min. Accepted entry format uses a period as the decimal separator, optional thousands grouping by commas, and no scientific notation. Higher Q raises differential pressure with the square of the flow ratio. The Flow rate unit selector supports L/min, m³/h, L/s, US gal/min, and ft³/min and converts the current value when changed. Avoid mixing a numeric value from one unit with a selector left on another.

Flow factor (Kv) is required and must be greater than 0; the demonstration uses 5 L/min so the Q/Kv ratio is exactly 2. The Flow factor unit supports the same flow-unit choices and is normalized independently. At fixed Q and specific gravity, a larger Kv reduces pressure differential because Kv is squared in the denominator. Zero is invalid because it would require division by zero. Confirm that your coefficient is genuinely compatible with the Kv-style relation before using it.

Differential pressure is required and nonnegative only when solving for flow; otherwise it is calculated. The Pressure unit selector supports bar, kPa, Pa, MPa, psi, and mmHg and converts the live value when changed. A 4 bar example corresponds to 400 kPa and about 58.015 psi. Pressure-unit conversion changes presentation, not the underlying physical state. Do not confuse gauge pressure at one point with a pressure difference between two points.

Output guide

The header summary pills labeled Mode, Fluid, and Specific gravity mirror the active solve direction and fluid assumptions so you can confirm context at a glance. Differential pressure is the pressure difference implied by Q, Kv, and S and is shown in the selected pressure unit. It is an equation-based estimate rather than a full piping-system loss calculation. Zero is valid when flow is zero. Volumetric flow rate shows Q in the selected flow unit; in Flow rate mode it is the rearranged estimate from ΔP, Kv, and S. Flow ratio Q / Kv is the dimensionless normalized ratio after both flow quantities are converted to the same base unit; it controls pressure quadratically. Specific gravity used confirms the exact S value in the model.

The Pressure equivalents table has two columns: Pressure unit and Equivalent value. Every row represents the same ΔP converted into a different unit, so the numbers should not be added or compared as separate losses. The Calculation audit table has Quantity, Canonical value, and Role in the model columns. It shows Q and Kv normalized to m³/h, their ratio, and S so you can see the exact ingredients used by the formula. These values also feed the exported workbook.

Worked example

With Water selected, S = 1.000. Set Q = 10 L/min and Kv = 5 L/min. Because both use the same flow unit, their normalized ratio is still 10 ÷ 5 = 2. Square that ratio to get 4, then multiply by specific gravity: ΔP = 2² × 1 = 4 bar. The first-open result therefore displays 4.00 bar. The equivalent table shows 400.0000 kPa, about 58.0151 psi, and 400000 Pa. If Q is doubled to 20 L/min while Kv and S remain unchanged, the ratio doubles and the calculated pressure rises by a factor of four to 16 bar.

Learn more

Specific gravity is a density ratio and therefore has no unit; for practical background and example liquid values, see Engineering ToolBox's density, specific weight, and specific gravity explanation. For SI terminology, the NIST definition of the pascal identifies Pa as the special name for N/m². Use manufacturer data and the applicable engineering standard when the coefficient depends on valve geometry, Reynolds number, viscosity, compressibility, or operating regime.