Linear Interpolation Imputation Calculator

Calculator Inputs

Enter ordered x,y pairs. Use blank, NA, N/A, NULL, MISSING, or ? for missing y values.

Dataset name

X-axis label

Y-axis label

Decimal precision

Edge handling

Missing tokens

Data points (x,y per line)

Example: 1,12 then 2,NA then 3,18

Sort data by x before processing

Example Data Table

Index	Observed Value	Completed Value	Explanation
1	12	12	Observed point remains unchanged.
2	Missing	15	Interpolated between index 1 and 4.
3	Missing	18	Interpolated on the same straight line.
4	21	21	Observed point remains unchanged.
5	24	24	Observed point remains unchanged.

This sample uses evenly spaced x positions, but any numeric x values are accepted.

Formula Used

Linear interpolation estimates a missing value from the two nearest observed points that surround it on the x-axis.

Imputation formula

y_m = y₁ + ((x_m - x₁) / (x₂ - x₁)) × (y₂ - y₁)

Where:

x_m is the position of the missing point.
(x₁, y₁) is the nearest known point before the gap.
(x₂, y₂) is the nearest known point after the gap.
The method assumes the change between known points is linear.

When edge handling is set to extrapolation, the calculator extends the nearest straight line beyond the first or last known point.

How to Use This Calculator

Enter your dataset name and axis labels.
Paste x,y rows into the data box, one pair per line.
Mark unknown y values with a blank or a missing token.
Choose decimal precision and edge handling mode.
Enable sorting if your x values are not already ordered.
Press Calculate Imputation to generate completed values.
Review the summary, completed table, and Plotly graph.
Download the finished table as CSV or PDF.

FAQs

1. What does this calculator do?

It fills missing numeric values using straight-line interpolation between surrounding observed points. It also reports unresolved edges, summarizes coverage, plots the completed series, and supports exports.

2. When should linear interpolation be used?

Use it when values change smoothly across an ordered index, such as time, distance, or sequence position. It works best when abrupt jumps are unlikely between known observations.

3. Can it fill multiple missing rows in one gap?

Yes. If several consecutive rows are missing between two known points, each missing value is placed proportionally along the same interpolated line segment.

4. What happens to missing values at the beginning or end?

That depends on edge handling. You can leave them unresolved, copy the nearest known value, or estimate them with linear extrapolation when enough known points exist.

5. Do x values need equal spacing?

No. The calculator accepts any numeric x values. Interpolation uses the actual distance between x positions, so uneven spacing is handled correctly.

6. Why are duplicate x values rejected?

Interpolation requires a unique position for each observation. Duplicate x values create ambiguous slopes and can distort both completed values and plotted results.

7. Can I use this for time-series data?

Yes. Many users map dates to numeric positions or ordered indices, then interpolate missing values across the series. It is especially useful for evenly sampled records.

8. What should I check after imputation?

Review whether the completed values follow a believable trend, confirm the chosen edge mode, and inspect unresolved rows before using the data in analysis or reporting.