What it does
In distance sampling you walk a line (or stand at a point) and, for every animal or group you detect, record how far it was from the line or point. Animals far away are more likely to be missed, so a plain count underestimates how many are there. The way detections thin out with distance tells you how many were missed, and this tool turns that into a density.
It fits two standard detection functions by maximum likelihood to your exact distances:
- Half-normal: g(x) = exp(−x²/2σ²), one parameter.
- Hazard-rate: g(x) = 1 − exp(−(x/σ)^−b), with a shape b that allows a flat “shoulder” near the line.
Both assume every animal on the line or point itself is seen (g(0) = 1). From the fit you get the effective strip width (lines) or effective detection radius (points), the average detection probability, and the density per km² and per hectare with a log-normal confidence interval (Buckland et al. 2001).
How to use it
- Choose Line transects or Point transects.
- Paste one row per detection: the name of the line or point, then the distance in metres (perpendicular distance from the line, or straight-line distance from the point). A single column of distances works too. You can also open a CSV or Excel file.
- For lines, give the length of each line in km with the same names. If you give one total length instead, the count variance is assumed Poisson. For points, give the number of points; points with no detections count as zeros.
- Set the truncation distance w. Leave it blank to use the farthest detection; trimming the farthest 5 to 10 % of detections usually gives a better fit.
- Choose the detection model (best by AIC, or one of the two) and the confidence level.
What each number means
- Effective strip width (ESW): the half-width of a strip in which, if every animal were seen, you would expect the same count. Density = n ÷ (2 × length × ESW).
- Effective detection radius: the same idea for points. Density = n ÷ (number of points × π × EDR²).
- Encounter rate: detections per km or per point. Its CV comes from the spread between lines or points when they are named.
- CI: log-normal, combining the count and detection-function uncertainty with Satterthwaite degrees of freedom, as in the program Distance.
Worked example
The line example is made up: six lines totalling 12 km and 61 detections. With w = 50 m, one detection is left out. The half-normal model has the lowest AIC (416.96, against 422.47 for the hazard-rate, ΔAIC 5.51). The page shows D = 128.9 per km² (95 % CI 91.54 to 181.5), or 1.289 per hectare. The effective strip width is 19.4 m ± 1.82 m, so an animal within 50 m has a 0.388 chance of being seen. The encounter rate is 5 per km, with a CV of 12.7 % between lines, and the interval uses 11.7 degrees of freedom.
The point example (also made up) has 26 detections within 80 m at 12 points. The hazard-rate model wins narrowly (ΔAIC 1.06), giving D = 703.8 per km² (95 % CI 273.2 to 1813) and an effective detection radius of 31.3 m; the half-normal gives 447.2 per km². When two models fit about equally well but disagree, more detections are needed.
Tips
- Aim for at least 60 to 80 detections for a reliable detection function.
- Measure distances accurately, especially near the line; rounding to 0 or to round numbers distorts the fit.
- If animals occur in groups, enter one row per group; the density is then of groups, which you multiply by the mean group size.
Frequently asked questions
Are adjustment terms or covariates supported? No. This tool fits the two key functions without adjustment terms, which covers many surveys; for more complex models use the free program Distance or the R package Distance.
What if animals move away before I see them? Distance sampling assumes they are recorded at their original position; responsive movement biases the result.
Is my data sent anywhere? No. Everything is worked out in your browser, and the page works offline once loaded.
Where the numbers come from
- Methods: S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers and L. Thomas, Introduction to Distance Sampling (Oxford University Press, 2001): detection functions, the likelihood for exact distances, encounter-rate variance, the delta method, the log-normal interval and Satterthwaite degrees of freedom. Hazard-rate model: Hayes and Buckland (1983). Formulas only; no tables are copied.
- Checked in the tests against an independent Python fit (SciPy 1.x optimize.minimize, integrate.quad, a finite-difference Hessian and stats.t) of the same data, and against the closed-form half-normal estimate σ² = mean of x² with no truncation.
- The examples are made up.
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Last updated 2026-11-09.