Understand the relationship
The reasoning behind the result
The ladder supplies the relationship for this run
A ladder contains independently known fragment lengths. Measuring its bands and the unknown samples in the same gel or consistently scaled image links migration x with fragment length L. This tool models linear double-stranded DNA; circular, supercoiled, single-stranded and RNA samples do not inherit that calibration automatically.
Matrix properties, field, buffer, conformation, sequence and measurement choices affect migration. The entered standards must be resolved and appropriate for the samples. A ladder name alone is insufficient: different products and conditions can give different band compositions and positions.
Local interpolation is linear in log length
y = log₁₀(L); f = (x − x₁)/(x₂ − x₁); L = 10^[(1 − f)y₁ + fy₂]
x₁ and x₂ are the measured positions of the adjacent bracketing standards, and y₁ and y₂ are their base-10 log lengths in the same unit. The fraction f tells how far the unknown lies between those positions. Interpolating the logs then exponentiating gives a geometric, rather than arithmetic, interpolation of lengths.
Halfway between 1,000 bp and 100 bp on this local migration scale, the estimate is √(1,000 × 100), about 316.23 bp; it is not their arithmetic mean of 550 bp. With more than two standards, the correct neighboring pair is selected separately for each sample.
A global log-linear fit is a declared approximation
b = Σ[(xi − x̄)(yi − ȳ)] / Σ(xi − x̄)²; yfit = ȳ + b(x − x̄)
The fitted option uses unweighted ordinary least squares, treating migration as the predictor and log length as the response. Every entered standard contributes equally. A centered computation improves numerical stability; fitted mean position, mean log size and slope are reported so the relationship can be reconstructed.
Log residuals show observed log length minus fitted log length. R² and RMS residual describe this particular calibration and do not provide a confidence interval or include uncertain band positions. A broad size range may be curved rather than log-linear; a high R² alone cannot prove the model is appropriate. Local interpolation likewise does not eliminate measurement error.
Inverse migration uses the same calibrated domain
x = x₁ + [(log₁₀ L − y₁)/(y₂ − y₁)](x₂ − x₁)
For a target fragment length, local inverse interpolation locates the expected position between its bracketing standards. The fitted inverse solves the fitted line. It is an expected position in the measured run or image, not a predicted run time or a universal migration rate.
Both directions stay inside the entered migration interval. In fitted mode the size limits are the fitted values at the two endpoint positions, which need not equal the observed endpoint sizes. Out-of-range records remain visible. Sizes below one base pair, indistinguishable positions and nondecreasing standard sizes are outside this DNA workflow's accepted domain.
Follow the numbers
Size one band and invert its calibration
- Two illustrative standards are measured from the same origin: 1,000 bp at 20 mm and 100 bp at 40 mm. Their log₁₀ lengths are 3 and 2.
- For a sample at 30 mm, f = (30 − 20)/(40 − 20) = 0.5. Its interpolated log length is 3 + 0.5 × (2 − 3) = 2.5.
- Exponentiating gives L = 10²·⁵ = 316.227766 bp, an approximate size rather than an exact count determined from sequence.
- Inverting that same target gives x = 20 + [(2.5 − 3)/(2 − 3)] × 20 = 30 mm. The calculation stays within the 20–40 mm calibration interval.
The forward and inverse estimates are two views of one explicitly local, same-run calibration.
Quick guide
How to use this calculator
- Identify the linear double-stranded DNA run and ladder. Enter actual known standard lengths and their measured migration from a common origin.
- Choose local interpolation or an explicit log-linear fit. Local interpolation needs two or more ordered standards; fitting needs at least three and should use a justified range.
- Enter named sample migrations to estimate sizes, or named target sizes to invert the same calibration. Keep image scaling and run conditions matched.
- Inspect every record, standard residual and model boundary. A result outside the migration domain is retained without extrapolation; a plausible estimate does not validate a band assignment.
Calculation method
Calculation and interpretation
Trace each DNA sizing estimate back to measured ladder positions and independently known fragment lengths.
y = log₁₀(L); y(x) = y₁ + [(x − x₁)/(x₂ − x₁)](y₂ − y₁); L = 10ʸ. A fitted model uses y = ȳ + b(x − x̄).
Worked example
Size one band and invert its calibration
The forward and inverse estimates are two views of one explicitly local, same-run calibration.
y = log₁₀(L); y(x) = y₁ + [(x − x₁)/(x₂ − x₁)](y₂ − y₁); L = 10ʸ. A fitted model uses y = ȳ + b(x − x̄).
Supported inputs
Precision and limits
Matched linear dsDNA only
Do not transfer this apparent-size calibration to mismatched gel conditions or different nucleic-acid structures. It does not identify fragments, confirm a sequence, resolve overlapping bands or analyze an uploaded image.
Bounded empirical estimates
No automatic ladder is supplied and no extrapolation is performed. Uncertainty in standards, migration measurement and model choice is not estimated. DNA standard and target inputs must represent at least one base pair. Numerical inputs support 10⁻⁹ through 10⁹ in their selected units; explicitly nonnegative positions and times also accept zero. These are calculation limits, not operating recommendations.
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