Calculator
Example data table
| Time | Observed Value | Missing? |
|---|---|---|
| 2026-01-01 | 120 | No |
| 2026-01-02 | — | Yes |
| 2026-01-03 | 128 | No |
| 2026-01-04 | 131 | No |
| 2026-01-05 | — | Yes |
| 2026-01-06 | 140 | No |
| 2026-01-07 | 144 | No |
Formula used
Linear interpolation
y = y₁ + ((x - x₁) / (x₂ - x₁)) × (y₂ - y₁)
Midpoint method
y = (y₁ + y₂) / 2 using the two surrounding observed values.
Nearest, previous, and next rules
Nearest picks the closest observed point. Previous carries the last observed value forward. Next carries the next observed value backward.
Natural cubic spline
Spline interpolation fits smooth cubic pieces between observed points, while forcing the second derivative to zero at both boundaries.
How to use this calculator
- Enter one time,value pair on each line.
- Leave missing values blank or write NA.
- Choose an interpolation method that matches your data behavior.
- Add an optional query time for a one-off estimate.
- Set decimal places and decide whether extrapolation is allowed.
- Press calculate to view results above the form.
- Use the CSV and PDF buttons to export the completed series.
Frequently asked questions
1. What data format should I paste?
Paste one time,value pair per line. Use commas, tabs, or semicolons. Time values can be numeric, dates, or datetimes. Missing values can stay blank or be written as NA.
2. Which interpolation method should I choose?
Use linear for steady transitions, spline for smoother curves, nearest for category-like behavior, previous or next for carry rules, and midpoint for simple gap filling between two surrounding observations.
3. What is extrapolation?
Extrapolation estimates values outside the observed time range. It can be useful for quick scenarios, but it is less reliable than interpolation because it extends patterns beyond known evidence.
4. Why can some rows stay unresolved?
Rows may remain unresolved when the selected method lacks enough surrounding observations and extrapolation is disabled. This usually happens at the start or end of the series.
5. Does the calculator change observed values?
No. Observed values stay untouched. The calculator only estimates rows marked as missing and shows whether each final number was original, interpolated, or unresolved.
6. Can I estimate a value at a custom time?
Yes. Enter a query time to estimate one additional point without changing the main series layout. The result appears in the summary and can also appear on the chart.
7. What does the chart show?
The chart compares observed points with the completed series after interpolation. This makes it easier to see filled gaps, overall direction, and the effect of the selected method.
8. Can I export the completed results?
Yes. Use the CSV button for spreadsheet work and the PDF button for reports or sharing. Exports include time labels, original values, completed values, and method notes.