Linear Interpolation Guide
Linear interpolation is a practical method for estimating a value between two known data points. It is used when the change between points is assumed to be steady. The calculator applies that idea to single points, reverse lookup, and data tables. It helps students, engineers, analysts, and researchers fill gaps without drawing a graph by hand.
Why Linear Interpolation Matters
Many measurements are stored at fixed intervals. A table may show values at 10 and 20 only. A project may need the value at 14.5. Linear interpolation treats the short interval as a straight line. That simple assumption is often accurate when the interval is small. It is also transparent, so each step can be checked.
What This Calculator Can Do
This tool supports two point interpolation and table based interpolation. You can solve for a missing y value from a target x value. You can also run the reverse calculation. That means the calculator can estimate x when a target y is known. The table mode chooses the nearest surrounding pair automatically. It also marks extrapolated results when the target falls outside the table range.
Accuracy And Limits
Linear interpolation is not a curve fitting method. It does not detect hidden bends between points. For smooth data, smaller intervals usually improve accuracy. For nonlinear data, results should be treated as estimates. The slope shown in the result helps you judge the local rate of change. A sudden slope change between intervals may suggest using more data.
Export And Review
The calculator presents the chosen points, ratio, slope, intercept, and final answer. These details make the result easier to audit. CSV export is useful for spreadsheets. PDF export is useful for reports, homework, and field notes. The example table also shows the correct input format.
Best Practices
Use data points that surround the target whenever possible. Keep x values unique in two point mode. For reverse lookup, keep y values monotonic in table mode. Avoid extrapolation unless you understand the risk. Check units before entering data. Round only after the final calculation. When many targets are needed, enter them as a list. The program calculates each row the same way. This keeps batch work consistent and reduces copying mistakes.