Susquehanna Valley Engineering Group, Inc.Engineering ApplicationsPractical tools for building performance
Menu
CommissioningAdvancedEquipment Curves

Three-Point Curve Interpolation Calculator

Evaluate the quadratic passing through three distinct user-entered curve points by Lagrange interpolation.

Why it matters: Visible geometry and quantity arithmetic improves field coordination and makes allowances available for review.

User inputs

Enter field measurements

10 inputs
Select I-P or SI units for the entire input set.
Axis unit such as gpm, cfm, rpm, or Hz.
Axis unit such as ft, in. w.g., kW, or efficiency percent.
x-unitsFirst x-coordinate.
y-unitsFirst y-coordinate.
x-unitsSecond x-coordinate.
y-unitsSecond y-coordinate.
x-unitsThird x-coordinate.
y-unitsThird y-coordinate.
x-unitsEvaluation coordinate.

Calculated result

Engineering evaluation

Calculation complete—verify project criteria
Three-point quadratic interpolation (y(x))93.75 y-units
Target x (x)
25 x-units

Engineering interpretation

The quadratic through the three entered points evaluates to 93.75 y-units at x=25.

Important limitations

  • Mathematical interpolation only. Confirm point order, curve shape, monotonicity, equipment operating limits, extrapolation risk, uncertainty, and manufacturer data.

Engineering knowledge center

Understand the calculation—not just the answer

2026-08-07 · Free Library
Governing relationships
y(x)=Σ[y_i Π_{j≠i}(x−x_j)/(x_i−x_j)]
displayed symbols: x_1, y_1, x_2, y_2, x_3, y_3
Current substitution

Lagrange terms=[0, 60, 0]; y(25)=93.75.

Calculation sequence

Step-by-step method

  1. Confirm dimensions, formula symbols, unit system, and measurement sources.
  2. Apply the displayed geometry, quantity, or field-control equation.
  3. Review allowances, tolerances, constructability, and governing project requirements.

Equation legend

Inputs and calculated quantities

x_1
Point 1 x-value — x-units
y_1
Point 1 y-value — y-units
x_2
Point 2 x-value — x-units
y_2
Point 2 y-value — y-units
x_3
Point 3 x-value — x-units
y_3
Point 3 y-value — y-units
x
Target x-value — x-units
y(x)
Three-point quadratic interpolation — y-units
x
Target x — x-units

Continue the evaluation

Related calculators

Linear Interpolation Fan System Curve Pump System Curve

Engineering calculation disclaimer

These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.

Read the full use and limitation statement