Calculation sequence
Step-by-step method
- Calculate the target fraction between the two x values.
- Calculate the straight-line slope.
- Add the proportional y change to the first known y value.
CommissioningBeginnerCross-Discipline Analysis
Linear Interpolation Calculator
Interpolate a dependent value between two known points using a straight-line relationship.
Why it matters: Transparent interpolation is useful for curves and tables when the interval is locally linear and the source permits it.
Calculated result
Engineering evaluation
Interpolated dependent value (y)18 y units
- Interpolation fraction (f)
- 0.4 0–1 within interval
- Line slope (m)
- 0.2 y units/x unit
Engineering interpretation
The linear estimate at x = 40 is y = 18. The target lies between the entered points.
Engineering knowledge center
Understand the calculation—not just the answer
Governing relationships
f = (x−x1)/(x2−x1)
m = (y2−y1)/(x2−x1)
y = y1+f(y2−y1)
Current substitution
f = (40−0)/(100−0) = 0.4; m = 0.2; y = 10+0.4(30−10) = 18.
Equation legend
Inputs and calculated quantities
- x1
- First independent value — x units
- y1
- First dependent value — y units
- x2
- Second independent value — x units
- y2
- Second dependent value — y units
- x
- Target independent value — x units
- y
- Interpolated dependent value — y units
- f
- Interpolation fraction — 0–1 within interval
- m
- Line slope — y units/x unit
Applications
How this calculation is used
Building design
Interpolate published engineering data within a valid interval.
Construction
Estimate an intermediate lookup value.
Commissioning
Interpolate a reference value for field comparison.
Quality controls
Assumptions and limitations
Assumptions
- Entered values represent the same stable operating condition.
- Measurements and reference values use consistent units and boundaries.
Limitations
- This is a screening and field-verification tool, not an automatic acceptance decision.
- Project criteria, manufacturer data, governing standards, and measurement uncertainty remain controlling.
Field use
Verification procedure
- Confirm the approved reference values and test boundary.
- Stabilize the system and record calibrated field measurements.
- Review calculation assumptions, uncertainty, and supporting evidence before disposition.
Common engineering mistakes
- Comparing readings taken at different loads, modes, or reference conditions.
- Treating a calculated status as proof of code, contract, or manufacturer compliance.
Technical basis
References and source standards
- NIST/SEMATECH e-Handbook of Statistical MethodsPublished reference for averages, variability, standard deviation, calibration, and engineering data analysis.
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