🌱 Calculators

Emergence Speed Index (Maguire)

Computes the seedling emergence speed index by the Maguire (1962) formula, the most widely used vigour test in seed analysis laboratories. The index sums, over each counting date, the number of seedlings that emerged on that day divided by the number of days since sowing: ESI = n1÷t1 + n2÷t2 + n3÷t3. Because early emergences enter the sum divided by a smaller number, the index rewards the lot that emerges fast and uniformly — two lots may end with the same final emergence percentage and have very different indices, and it is that difference which predicts field performance. The convention adopted is Maguire's original one: each count takes the NEW seedlings of that day, not the cumulative total; using the cumulative total inflates the index because it counts the same seedling several times. This version works with three counting dates. Enter the number of new seedlings and the day of each of the three counts.

New seedlings at count 1 (units) Days after sowing of count 1 (days) New seedlings at count 2 (units) Days after sowing of count 2 (days) New seedlings at count 3 (units) Days after sowing of count 3 (days)

Result

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Maguire Emergence Index: Putting a Number on Seed Vigour

Two seed lots finish the test at 90% emergence and still behave very differently in the field. Final percentage saturates: it cannot tell the lot that came up inside five days from the one that dragged emergence out over a fortnight, and that delay is exactly what exposes seedlings to soil crusting, damping-off fungi and weed competition. Laboratory analysts and breeding researchers need a figure that captures speed, and the Maguire index has been the workhorse for that job since 1962.

The arithmetic is a plain sum: ESI = n1÷t1 + n2÷t2 + n3÷t3, where each n is the count of new seedlings on that date and each t the number of days since sowing. With the values on screen — 12 seedlings on day five, 25 on day seven and 8 on day ten — the terms work out at 2.400, 3.571 and 0.800, and the index closes at 6.771. Watch what the divisor does: those 25 seedlings on day seven carry more weight than all 45 would if they had turned up together on day ten. We follow the original Maguire convention of new counts; cumulative totals return 12.186 on the same data, nearly double.

The index carries no normalization by the number of seeds sown, so it compares treatments only within one experiment run at the same seeds per replicate — commonly 50 seeds in four replicates. It also depends on counting frequency: daily counts and every-other-day counts return different values from identical seed. Its unit is seedlings per day, never dimensionless. And because speed and total get blended into a single figure, report it beside the final emergence percentage and the mean emergence time, or a fast thin lot will tie with a slow full one.

Frequently asked questions

Do I enter new counts or cumulative counts?

New counts, meaning only the seedlings that emerged since the previous reading. That is how Maguire defined the index in 1962, and the difference is large: the sample values of 12, 25 and 8 new seedlings give 6.771, while entering cumulative totals of 12, 37 and 45 returns 12.186. Cumulative figures inflate the result because each seedling gets counted again on every later date. Most field sheets record running totals, so it pays to check and subtract before typing anything here.

I made six counts and the screen takes only three.

Because the index is a pure sum of independent terms, run it twice: compute with the first three dates, note the result, compute with the last three and add the two figures. The total matches what a six-term formula would produce. The same trick covers the opposite case — with only two counting dates, fill the third with zero seedlings and any day count above zero, since zero divided by anything leaves the sum untouched.

Is 6.771 a high index?

On its own it tells you nothing. The value depends on how many seeds were sown and how often you counted, so it only means something next to the control and the other treatments of the same trial, measured the same way. In the example, 45 seedlings out of a likely 50 emerged between day five and day ten, peaking on day seven, which reads as a strong lot. Had those same 45 arrived three days later, the index would drop to about 4.6 with an identical final percentage.

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Net Assimilation Rate (Gregory Formula)

Computes the net assimilation rate of a plant by the classic Gregory formula, the core of plant growth analysis. The rate is the dry matter gain per day multiplied by the ratio between the difference of the natural logarithms of the two leaf areas and the difference of the areas themselves: NAR = [(W2 − W1) ÷ interval] × [ln(A2) − ln(A1)] ÷ (A2 − A1). The result measures net photosynthetic efficiency per unit of leaf area, with respiration already discounted — typical values for annual crops in full growth lie between 5 and 15 grams per square metre of leaf per day, and a decline along the cycle indicates canopy self-shading. Gregory's (1926) logarithmic form was adopted rather than the approximation NAR = mass gain ÷ (mean leaf area × interval), because the former is exact when leaf area grows linearly with dry mass over the interval, which is the standard assumption of classic growth analysis. Enter the initial and final dry masses, the initial and final leaf areas and the interval between the two samplings.

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Seed Cultural Value

Computes the cultural value of a seed lot, CV = purity × germination ÷ 100, with both percentages taken from the laboratory analysis report. The result is the percentage of the lot's weight that is pure, live seed — what will actually become a plant: a lot with 98.5% purity and 92% germination delivers 90.6% useful seed, and the remaining 9.4% is inert matter and dead seed you are paying for. It is the basis for correcting the seeding rate (target kg/ha ÷ CV × 100) and for comparing prices between lots of different quality; the English equivalent is pure live seed (PLS). Enter the physical purity and the germination percentage.

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Crop Growth Rate (CGR)

Computes the crop growth rate, CGR = (W₂ − W₁) ÷ (Δt × A), the canopy's dry-matter gain per unit of ground area per day between two destructive samplings. Unlike relative growth rate, which measures efficiency per gram of existing plant, CGR measures the productivity of the LAND — it is what you compare across row spacings, seeding densities and fertiliser levels, because it answers how much biomass each square metre of field produces per day. Peak values in well-managed C4 crops fall around 20 to 30 g/(m²·day), and the integral of the CGR curve over the season is total biological yield. Enter the initial and final dry masses, the interval between samplings and the ground area sampled.

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Stand Density Index (Reineke)

Computes Reineke's stand density index, SDI = trees per hectare × (quadratic mean diameter ÷ 25)^1.605, which expresses the stocking of a forest stand as the equivalent number of trees per hectare it would hold if every one measured 25 cm DBH — the 10 inches of the original 1933 work, rounded in the metric version. The exponent 1.605 is the slope of the self-thinning line Reineke fitted empirically, and it is precisely what makes the index nearly independent of age and site quality, unlike a plain trees-per-hectare count. The number guides thinning decisions when compared with the species maximum SDI, which for most species falls between 1,000 and 1,200: competition mortality typically starts around 55% to 60% of the maximum, and the recommended management zone runs from 35% to 55%. In the example, 559 against a maximum of 1,100 gives about 51%, meaning the stand is still below the self-thinning threshold but already at the top of the management zone. Enter the number of trees per hectare and the quadratic mean diameter.

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Compute heat index from temperature (°C) and relative humidity (NOAA, valid for T ≥ 27°C).

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Larson-Skold Index (Water Corrosivity)

Computes the Larson-Skold index, the ratio between the aggressive and the protective anions in a water: chloride plus sulphate divided by alkalinity, all converted to milliequivalents per litre with the equivalent weights 35.45 for chloride, 48.03 for sulphate and 50.04 for alkalinity expressed as CaCO₃. The reading is direct: below 0.8 alkalinity dominates and the carbonate film protects carbon steel; between 0.8 and 1.2 corrosion stops being negligible; above 1.2 chloride and sulphate break the film and the localised corrosion rate takes off, the typical scenario of cooling tower makeup water running at many cycles of concentration. Unlike the Langelier index, this one does not say whether the water will scale — it measures only the corrosive power of the anions, which is why the two readings complement each other rather than compete. Total alkalinity was adopted as the input, instead of separate bicarbonate and carbonate, because that is what a routine laboratory reports, and converting it through the CaCO₃ equivalent returns exactly the sum of the two in milliequivalents per litre. Enter the chloride, the sulphate and the total alkalinity.

The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.