Time-Series Interpolation Utility — Free Linear & Spline Tool

This tool estimates values between observations in a time series. Sensors miss readings, surveys skip weeks, and experiments record at irregular times — yet analysis often needs a value at a time nobody measured. You paste time-value points, choose linear interpolation (a straight line between neighbours) or a smooth Catmull-Rom spline (a curve that bends gently through the points), and query any time. The tool deliberately refuses to extrapolate: a query beyond the observed range returns the nearest endpoint value with a warning, because guessing beyond data is forecasting, not interpolation, and deserves its own method and uncertainty.

How to use it

Paste points as time, value, one per line.
Choose linear or smooth spline.
Enter the query time.
Click Interpolate.
Flag interpolated values in your dataset so they are never mistaken for measurements.

Worked example

A temperature logger records 10 degrees at hour 0, 12 at hour 1, 11 at hour 2, and 15 at hour 3, with hour 1.5 missing. Linear interpolation gives 11.5 at hour 1.5 — the midpoint of 12 and 11. The spline gives a nearby but slightly different value, bending with the shape of neighbouring points. For a daily average, either is defensible; for detecting a sharp event, neither replaces a real reading. The honest move is to mark hour 1.5 as interpolated in the dataset and to report how many values in the analysis were interpolated rather than measured.

Honest limits

Interpolation assumes the underlying process moves smoothly between observations. It fails for abrupt changes — a sensor knocked offline during a spike, a stock price jumping on news, a patient crashing between rounds — where a straight line or smooth curve invents a calm passage that never happened. Long gaps are worse than short ones: interpolating across a week of missing data pretends to knowledge nobody has. Spline curves can also overshoot, dipping below or above neighbouring values in ways the real process never did. When gaps are long or the process is jumpy, report the gap as missing instead of filling it.

Who it is for

This tool is for researchers aligning irregular series to a common timeline, analysts filling short sensor gaps, and students learning the difference between interpolation and extrapolation. It is a gap-filler for short, smooth gaps — not a forecasting tool and not a substitute for missing measurements.

Going further

Keep interpolated values visibly distinct in every downstream product: a flag column in the dataset, a dashed line or hollow marker in charts, and a methods sentence stating the method and the fraction interpolated. Readers who cannot tell measured from filled values will over-trust the series, especially around the filled stretches. If more than about a fifth of a series is interpolated, reconsider whether the analysis is about the data or about the interpolation method — at that point, methods for missing data, such as multiple imputation with uncertainty, are more honest than a single filled line, however smooth it looks. When series must align to a common timeline — say, hourly sensor data against daily survey responses — interpolate the denser series onto the sparser one’s timestamps, not the other way around, so you invent as few values as possible. Document the alignment rule with the data: which series was interpolated, which method, and how many points were filled. A downstream analyst who sees a perfectly regular series with no gaps will assume it was measured that way; a short methods note prevents that misunderstanding and lets them judge whether the alignment choices affect the conclusions they draw. For reporting, state the interpolation method and the longest gap filled, not just the fact that gaps were filled. A series with ten one-hour gaps filled linearly is a different evidentiary claim from a series with one ten-day gap filled the same way, even though both are “interpolated.” Reviewers who see the longest gap can judge whether the conclusions survive it; reviewers who see only a blanket statement cannot. Transparency about the worst gap, not the average one, is what makes interpolated results believable.

Embed this tool on your website — free

Copy the code below to add this working tool to your own page. A small credit link stays with it — that’s all we ask.