MathBench

Plot Digitizer

Got a chart as a picture — a paper's figure, an old report, a screenshot — and need the numbers back? Load it, click four axis reference points, then click your data points and export CSV. Everything runs in your browser; nothing is uploaded.

Load a chart image to begin Choose a file, drag one here, or paste a screenshot (Ctrl+V)

How it works

Four steps, all visible above. Load the chart — file picker, drag-and-drop, or paste a screenshot straight from the clipboard. Calibrate: type the true values of two reference points on each axis (gridline intersections and axis endpoints work best), then click those four spots on the image; the magnifier gives you pixel-level aim. Pick: click each data point — the running table converts every click through the calibration instantly, so a mis-entered axis value can be fixed at any time and all points recompute. Export: CSV file, or tab-separated copy that pastes directly into any spreadsheet.

The method

s = (p − A₁) · (A₂ − A₁) ÷ |A₂ − A₁|²      (projection along the axis)

linear axis:  value = v₁ + s (v₂ − v₁)
log axis:     value = 10^( log v₁ + s (log v₂ − log v₁) )

Each clicked pixel is projected onto the direction of the calibrated axis, and its position along that direction is interpolated between the two reference values — in log space for logarithmic axes. Because projection follows the axis direction you clicked rather than the image's pixel rows, a uniformly rotated scan digitizes correctly. This is the standard manual-digitizing methodology used by tools like Rohatgi's WebPlotDigitizer, widely cited in academic data-extraction work; perspective distortion is the one thing it cannot undo.

Worked example

Suppose you calibrate X1 = 0 at pixel 100 and X2 = 10 at pixel 600, and then click a point at pixel 350 (same height as the axis):

  1. Projection: s = (350 − 100) ÷ (600 − 100) = 0.5
  2. Value: 0 + 0.5 × (10 − 0) = x = 5.0

On a log axis calibrated 10 → 1,000 over the same pixels, that midpoint click instead returns 10^(1 + 0.5 × 2) = 100— the geometric middle, exactly as a log scale demands. One pixel of click error at this calibration is 10 ÷ 500 = 0.02 on the linear axis — which is also your honest precision limit.

Getting clean data

  • Calibrate wide. Reference points at opposite ends of each axis divide your click error by the longest possible baseline. Never calibrate on two adjacent gridlines.
  • Use gridline intersections as reference points when the axis labels sit away from the axis line — the intersection is the truth, the label is typography.
  • Feed it the biggest image you have. Precision is pixels; a 2× larger screenshot is 2× more precise. Zoom the source before screenshotting.
  • Click marker centers, not edges — and for fat markers, the loupe's crosshair makes center-finding honest.
  • Report digitized data as digitized. In academic use, cite the original figure and note the extraction method — standard practice, and the values are estimates of the original data, not the data itself.

Frequently asked questions

Is my image uploaded anywhere?

No. The image is drawn onto a canvas in your own browser and never leaves your machine — there is no server side to this tool at all. Close the tab and everything is gone, which also means: export your data before you leave.

How accurate is manual digitizing?

Bounded by pixels: if your x-axis spans 500 pixels, each pixel is 0.2 percent of the range, and a careful click with the magnifier lands within a pixel or two. Calibration is the bigger lever — clicking reference points far apart divides that error over a longer baseline. Expect extracted values good to a fraction of a percent from a clean chart, and treat anything beyond three significant figures as decoration.

Can it handle logarithmic axes?

Yes — tick the log box for either axis and the interpolation happens in log space: position along the axis maps to equal ratios rather than equal differences. Calibrate on clean decade lines (10 and 1,000 beat 37 and 8,214) and the extracted values will honor the scale exactly.

What about rotated or skewed images?

A uniformly rotated scan is fine: values are computed by projecting each click onto the axis directions you calibrated, so a chart that is tilted a few degrees digitizes correctly as long as you click the calibration points on the actual axes. Perspective distortion — a photo taken at an angle — is not corrected; straighten those in a photo editor first.

How does this compare to automatic tools like WebPlotDigitizer?

This is the fast manual path: four calibration clicks and one click per point, with nothing to install. Dedicated tools such as WebPlotDigitizer add automatic curve tracing, color-based extraction, and map projections — worth the setup for hundreds of points. For pulling a dozen values out of a paper's figure, manual clicking is usually quicker than configuring the robot.

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