Seed Germination Probability Calculator

Expected plants and enough plants are different questions

Dividing your target by germination rate gives a count that meets the target on average. It does not give a chosen probability of actually having enough plants. This calculator compares that expectation-only count with the smallest sowing count that reaches your selected probability. It then rounds tray purchases, not the seed recommendation, assuming one seed per cell.

Method: independent successes and a binomial tail

Let g be germination fraction and s the survival fraction among germinated seeds. Per-seed probability of a transplant-ready plant is p = g x s. If K is the target and n seeds are sown independently with that same p, X follows a binomial distribution. Probability of enough plants is P(X at least K) = 1 - sum from j = 0 to K - 1 of [C(n,j) x p^j x (1 - p)^(n - j)].

The production calculation updates a probability distribution one seed at a time, with a final state holding all outcomes at or above K. This avoids large factorials and subtractive cancellation. It stops at the first whole n reaching the requested probability, with a 10,000-seed search ceiling. A plan beyond that ceiling produces a visible error rather than a misleading seed count.

Expectation-only seeds = ceil(K / p). Expected ready plants at the probability-based count = n x p. Whole trays = ceil(n / usable cells per tray); unseeded cells = trays x cells - n. Cost = n x cost per seed. The result does not add the unseeded cells to the sowing recommendation.

Worked example: three plants from a low-germination lot

For 3 target plants, 50% germination, and 100% survival among sprouts, p = 0.5. The expectation-only count is 6 seeds. At 10 seeds, the probability of at least 3 ready plants is 94.53125%, below a 95% target. At 11 seeds it is 96.728515625%, so 11 is the minimum recommended count. Expected ready plants are 5.5. Two 6-cell trays hold those seeds with 1 unseeded cell; at $0.10 per seed the seed cost is $1.10.

Use the probability as a conditional planning result

The displayed percentage is only as trustworthy as p and the independence assumption. A shared cold tray, damping-off outbreak, drying event, or incorrect growing conditions can affect many seeds together. Such correlated losses can make the binomial model too optimistic. Increasing the probability target does not fix a poor rate estimate or shared environmental risk.

Use a recent lot test and realistic seedling-survival observations under similar conditions. Compare a lower germination or survival input as a sensitivity check. This tool does not estimate uncertainty in a small germination test, distinguish crop varieties, predict germination dates, or recommend treatment, temperature, sowing depth, or chemicals.

Bounds and sources

Targets support 1-200 plants, rates 0-100%, probability targets 50-99.9%, 1-200 cells per tray, and $0-$10 per seed. Zero success is infeasible and is explicitly rejected. A 100% combined success rate needs exactly K seeds; probability targets below 100% avoid claiming certainty for imperfect rates.

The binomial calculation is self-contained probability arithmetic, not an empirical crop formula, so no external authority is needed for its mathematics. Johnny's planting calculators and tools provide broader crop and seasonal planning context (undated collection); this tool deliberately uses your own rates rather than importing crop presets.

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Last updated: 2026-10-09. Conditional probability estimate, not a crop success guarantee.