Gel Band Size Estimation (DNA bp / Protein kDa, Semi-log Standard Curve)
Measure the migration distance of a band on a gel and want to know its size — the approach is to fit a standard curve using the marker. The key is what coordinate system the curve is plotted in:
log10(size) = a × migration distance + b
Migration distance is linear with the log of size, not with size itself. This determines the two issues described below.
1. Linear interpolation between two marker bands always overestimates
Suppose two adjacent marker bands are 10,000 bp and 1,000 bp, and your band falls exactly midway between them.
| Method | Result |
|---|---|
Linear interpolation on size: (10000 + 1000) / 2 |
5500 bp |
Correct: interpolate in log space — geometric mean √(10000 × 1000) |
3162 bp |
74% too high. The bias is directional: linear interpolation always overestimates because the logarithm is a concave function. The wider the interval between bands, the larger the error — a 10-fold span gives 74% overestimation; a 2-fold span gives about 6%.
Six percent may sound small, but it is systematic: every band on the same gel is biased in the same direction. This tool shows both results side by side so you can see the discrepancy on your gel.
2. Beyond the marker range, you have extrapolation — not estimation
The semi-log relationship holds only over a limited range and breaks down at both ends:
- For very large DNA, the radius of gyration exceeds the gel pore size. Fragments of different sizes co-migrate to the same position and cannot be resolved. The curve flattens; migration distance carries essentially no size information.
- For protein SDS-PAGE, the complete log(molecular weight) vs. Rf curve is actually S-shaped — very large molecules cannot enter the gel, very small ones are barely sieved, and only the middle section is approximately linear. Where that linear segment falls depends on gel concentration.
Therefore, when a band runs beyond the outermost marker band, the result is extrapolation, not an estimate, and should not be trusted. This tool explicitly flags which bands fall outside the marker range.
3. For proteins, use Rf — not raw migration distance
Standard practice in protein SDS-PAGE is to divide migration distance by the dye-front migration distance to obtain the relative migration rate, Rf:
Rf = band migration distance ÷ dye-front migration distance
This removes run-to-run variation from time, voltage, and gel length. Raw distances are not comparable across gels run on different days; Rf values are. This tool converts automatically when you supply the dye-front distance.
4. The R² of the standard curve tells you whether this gel is usable
If the marker points do not fall on a straight line, the run itself has a problem: uneven gel, distorted loading wells, unstable voltage, or imprecise distance measurements. Estimates for unknown bands are then equally unreliable — no amount of careful arithmetic will rescue a bad gel. This tool reports R² and the residual for each marker band.
Data sources
That migration distance is linear with log(size), that large DNA co-migrates when the radius of gyration exceeds pore size, that the complete log(MW) vs. Rf curve for proteins is S-shaped with only the middle segment approximately linear, and that the linear range shifts with gel concentration — these are standard conclusions in electrophoresis methodology, found in reference texts on gel electrophoresis and technical bulletins on protein molecular weight determination. This tool introduces no empirical constants; the standard curve is fitted entirely from your own marker data.
Related tools
Linear regression and back-calculation of unknowns from a standard curve: Standard Curve Calculator; Vector and insert amounts for ligation reactions: Ligation Calculator; Restriction enzyme recognition sequences and cut sites: Restriction Enzyme Browser; FASTA length distribution and N50: FASTA Statistics.
FAQ
Why can't I linearly interpolate between two marker bands?
Because migration distance corresponds to the **logarithm** of size, not to size itself. The midpoint between bands at 10,000 bp and 1,000 bp is the geometric mean: √(10,000 × 1,000) = 3,162 bp. Linear interpolation gives 5,500 bp — 74% too high. The logarithm is a concave function, so this bias always runs in one direction: too large. The wider the interval, the larger the error: a 10-fold span gives 74% overestimation; a 2-fold span gives about 6%. Six percent may not sound like much, but it is systematic — every band on the same gel is biased in the same direction.
My band runs beyond the outermost marker band. Can I still estimate its size?
No — that is extrapolation, not estimation. The semi-log relationship holds only over a limited range: when DNA molecules are large enough that the radius of gyration exceeds the gel pore size, fragments of different sizes co-migrate to the same position and cannot be resolved. For protein SDS-PAGE, the complete log(MW) vs. Rf curve is S-shaped and flat at both ends. The correct approach is to switch to a marker with a wider range, or to adjust gel concentration and run time so the target band falls within the middle of the marker range.
Why does protein SDS-PAGE use Rf rather than raw migration distance?
Rf = band migration distance ÷ dye-front migration distance. Dividing by the dye front removes run-to-run variation from time, voltage, and gel length — raw distances are not comparable across gels run on different days, but Rf values are. This tool converts automatically when you supply the dye-front distance; the same applies to DNA when comparing across gels.
What R² is acceptable for the standard curve?
Generally 0.99 or above. A lower R² means the marker points do not fall on a straight line, which usually points to a problem with the run itself: uneven gel, distorted loading wells, unstable voltage, or imprecise distance measurements. In that case, estimates for unknown bands are equally unreliable — careful arithmetic cannot rescue a bad gel. Re-run it. This tool lists what each marker band back-calculates to and its percentage deviation, to help identify which band is off.
How many marker bands are needed at minimum?
Two is mathematically sufficient to fit a line, but gives no way to assess linearity. At least five bands are recommended, and they should **bracket the unknown bands on both sides** — if the unknown falls between marker bands it is interpolation; if it falls outside, it is extrapolation. This tool requires at least three bands.
Can bands in different lanes on the same gel be compared directly?
Bands in different lanes of the same gel, run in one session, are broadly comparable, but edge lanes often show a smiling effect (faster or slower at the edges), so measure distances carefully. Cross-gel comparison always requires Rf. Also decide consistently where to measure thick bands — centre or leading edge — and apply the same rule across the entire gel.
How many significant figures should I report for the estimated size?
Do not report more precision than the data support; three significant figures is usually already too many. Distance measurements carry an uncertainty of a fraction of a millimetre, which gets amplified exponentially when converting to size; the closer the band is to the edge of the marker range, the larger the size uncertainty for a given distance error. This tool shows more decimal places than you would normally report so that you can see the difference between algorithms — round appropriately when reporting results.
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