Calculator Inputs
Paste a DNA sequence to auto-count bases, or leave it blank and enter counts manually. The calculator normalizes base frequencies if they do not sum to 1.
Example Data Table
| DNA Pattern | Base Frequencies (A/C/G/T) | Comparisons | Exact Probability | At Least One Match |
|---|---|---|---|---|
| ATGCATGC | 0.25 / 0.25 / 0.25 / 0.25 | 10,000 | 1.525879e-5 | 0.141517 |
| AAAAATTT | 0.30 / 0.20 / 0.20 / 0.30 | 50,000 | 5.314410e-5 | 0.929996 |
| GGCCGGCCAA | 0.20 / 0.30 / 0.30 / 0.20 | 200,000 | 2.125764e-6 | 0.346202 |
Formula Used
1) Exact sequence probability
For a sequence with counts of A, C, G, and T: P = p(A)a × p(C)c × p(G)g × p(T)t
2) Expected matches across comparisons
E(X) = n × P, where n is the number of independent sequence comparisons.
3) Probability of at least one match
P(X ≥ 1) = 1 − (1 − P)n
4) Binomial probability of exactly k matches
P(X = k) = C(n, k) × Pk × (1 − P)n−k
5) Self-information in bits
I = −log2(P). Larger values indicate rarer sequence events.
How to Use This Calculator
- Paste a DNA sequence if you want automatic A, C, G, and T counting.
- Leave the sequence blank if you prefer manual base counts.
- Enter the nucleotide frequencies for your experiment, mixture, or population.
- Add the number of independent comparisons, windows, or database checks.
- Choose the exact match count needed for the binomial output line.
- Press calculate to show results above the form.
- Review the probability table and distribution chart.
- Use the CSV or PDF buttons to export the current result set.
Frequently Asked Questions
1) What does exact sequence probability mean?
It is the probability that one random DNA sequence has the same base composition and ordered pattern you defined, under the selected nucleotide frequencies.
2) Why can one-in odds become extremely large?
Longer sequences multiply many small probabilities together. That makes exact matches rare, so the inverse probability becomes a very large one-in value.
3) What does the comparison count represent?
It represents the number of independent opportunities for the target sequence to appear, such as database checks, genome windows, or separate random draws.
4) Can I use a typed DNA sequence instead of counts?
Yes. When a valid sequence is pasted, the calculator automatically counts A, C, G, and T and uses those values for the probability model.
5) What happens if base frequencies do not sum to 1?
The calculator rescales them automatically. This keeps relative proportions while making the total valid for probability calculations.
6) What does the chart show?
The chart plots the binomial probability distribution for observing different exact match counts across your comparison set, based on the calculated single-sequence match probability.
7) Is this useful for chemistry and molecular analysis?
Yes. It helps when modeling nucleotide mixtures, sequence rarity, assay specificity, library screening, and random-match expectations in molecular chemistry workflows.
8) Does this model account for sequence dependence?
No. It assumes independent draws based on the chosen base frequencies. Real genomes may contain repeats, context effects, and dependencies not captured here.