Agronomy Formulas
Calculations, Equations & Numericals
Seed & Plant Population
| Parameter | Formula & Details |
|---|---|
| Plant Population |
$$\text{Plant Population} = \frac{\text{Field Area (m}^2\text{)}}{\text{Row Spacing (m)} \times \text{Plant Spacing (m)}}$$
For 1 Ha: Area = $10,000\text{ m}^2$
|
| Seed Rate |
$$\text{Seed Rate (kg/ha)} = \frac{\text{Plant Pop.} \times \text{Test Wt (g)} \times 100}{\text{Germination (\%) } \times \text{Purity (\%) } \times 1000}$$
|
| Seed Rate (Shortcut) |
$$\text{Seed Rate} = \frac{\text{Recommended Seed Rate} \times 100}{\text{Germination (\%) } \times \text{Purity (\%) }}$$
|
| Germination (%) |
$$\text{Germination (\%)} = \left(\frac{\text{Normal Seedlings}}{\text{Total Seeds}}\right) \times 100$$
|
| Purity (%) |
$$\text{Purity (\%)} = \left(\frac{\text{Pure Seed Weight}}{\text{Total Sample Weight}}\right) \times 100$$
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| Seedling Vigour Index (SVI) |
$$\text{SVI} = \text{Germination (\%) } \times \text{Seedling Length}$$
|
Crop Yield & Field Metrics
| Parameter | Formula |
|---|---|
| Grain Yield (kg/ha) |
$$\text{Yield (kg/ha)} = \frac{\text{Plot Yield} \times 10,000}{\text{Plot Area (m}^2\text{)}}$$
|
| Biological Yield |
$$\text{Biological Yield} = \text{Grain Yield} + \text{Straw Yield}$$
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| Straw Yield |
$$\text{Straw Yield} = \text{Biological Yield} – \text{Economic Yield}$$
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| Harvest Index (HI) |
$$\text{HI} = \left(\frac{\text{Economic Yield}}{\text{Biological Yield}}\right) \times 100$$
|
| Shelling Percentage |
$$\text{Shelling (\%)} = \left(\frac{\text{Grain Weight}}{\text{Pod / Ear Weight}}\right) \times 100$$
|
Fertilizer & Herbicide Inputs
| Parameter | Formula |
|---|---|
| Fertilizer Required |
$$\text{Fertilizer (kg)} = \frac{\text{Nutrient Required} \times 100}{\text{\% Nutrient in Fertilizer}}$$
|
| Nutrient Supplied |
$$\text{Nutrient} = \frac{\text{Fertilizer Amount} \times \text{\% Nutrient}}{100}$$
|
| Herbicide Quantity |
$$\text{Commercial Product} = \frac{\text{Required a.i.} \times 100}{\text{\% a.i.}}$$
|
💡 Practical Example
To supply 60 kg N using Urea (46% N):
$\text{Urea Required} = \frac{60 \times 100}{46} = \mathbf{130.4\text{ \textbf{kg}}}$
Weed Management Indices
| Index Name | Formula & Details |
|---|---|
| Weed Control Efficiency (WCE) |
$$\text{WCE (\%)} = \left(\frac{\text{DMC} – \text{DMT}}{\text{DMC}}\right) \times 100$$
|
| Weed Index (WI) |
$$\text{WI (\%)} = \left(\frac{Y_{WF} – Y_T}{Y_{WF}}\right) \times 100$$
|
| Weed Smothering Efficiency (WSE) |
$$\text{WSE (\%)} = \left(\frac{WD_{\text{sole}} – WD_{\text{intercrop}}}{WD_{\text{sole}}}\right) \times 100$$
|
Intercropping & Competition
| Parameter | Formula |
|---|---|
| Land Equivalent Ratio (LER) |
$$\text{LER} = \left(\frac{Y_{ab}}{Y_{aa}}\right) + \left(\frac{Y_{ba}}{Y_{bb}}\right)$$
|
| Relative Crowding Coeff. (K) |
$$K = \frac{\text{Mixed Yield} \times \text{Pure Proportion}}{(\text{Pure Yield} – \text{Mixed Yield}) \times \text{Mixed Proportion}}$$
|
| Aggressivity (A) |
$$A = \text{Relative Yield}_A – \text{Relative Yield}_B$$
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| Competition Ratio (CR) |
$$\text{CR} = \left(\frac{\text{LER}_A}{\text{LER}_B}\right) \times \left(\frac{Z_B}{Z_A}\right)$$
|
| Relative Yield Total (RYT) |
$$\text{RYT} = \text{RY}_A + \text{RY}_B$$
|
📊 LER Interpretation Guide
• LER > 1: Yield Advantage (Intercropping Beneficial)
• LER = 1: No Advantage
• LER < 1: Yield Loss (Mutual Competition)
Soil Physical Properties
| Parameter | Formula & Standard Values |
|---|---|
| Bulk Density (BD) |
$$\text{BD} = \frac{\text{Dry Soil Mass}}{\text{Bulk Soil Volume}}$$
Standard Unit: $\text{g/cm}^3$
|
| Particle Density (PD) |
$$\text{PD} = \frac{\text{Dry Soil Mass}}{\text{Particle Volume}}$$
Avg: $2.65\text{ g/cm}^3$
|
| Porosity (%) |
$$\text{Porosity (\%)} = \left[1 – \left(\frac{\text{BD}}{\text{PD}}\right)\right] \times 100$$
|
| Void Ratio (e) |
$$e = \frac{\text{Porosity}}{100 – \text{Porosity}}$$
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Soil Moisture & Irrigation
| Parameter | Formula |
|---|---|
| Gravimetric Moisture (%) |
$$\text{Moisture (\%)} = \left(\frac{\text{Wet Weight} – \text{Dry Weight}}{\text{Dry Weight}}\right) \times 100$$
|
| Volumetric Moisture ($\theta_v$) |
$$\theta_v = \theta_g \times \text{BD}$$
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| Field Capacity (FC %) |
$$\text{FC (\%)} = \left(\frac{\text{Weight at FC} – \text{Oven Dry Weight}}{\text{Oven Dry Weight}}\right) \times 100$$
|
| Available Water (%) |
$$\text{AW} = \text{Field Capacity (FC)} – \text{PWP}$$
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| Water Use Efficiency (WUE) |
$$\text{WUE} = \frac{\text{Grain Yield}}{\text{Consumptive Water Use}}$$
|
| Irrigation WUE (IWUE) |
$$\text{IWUE} = \frac{\text{Yield}}{\text{Irrigation Water Applied}}$$
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Crop Growth Analysis
| Parameter | Formula |
|---|---|
| Crop Growth Rate (CGR) |
$$\text{CGR} = \frac{W_2 – W_1}{(T_2 – T_1) \times \text{Ground Area}}$$
|
| Relative Growth Rate (RGR) |
$$\text{RGR} = \frac{\ln W_2 – \ln W_1}{T_2 – T_1}$$
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| Net Assimilation Rate (NAR) |
$$\text{NAR} = \frac{(W_2 – W_1)(\ln L_2 – \ln L_1)}{(L_2 – L_1)(T_2 – T_1)}$$
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| Leaf Area Index (LAI) |
$$\text{LAI} = \frac{\text{Leaf Area}}{\text{Ground Area}}$$
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| Leaf Area Duration (LAD) |
$$\text{LAD} = \left(\frac{\text{LAI}_1 + \text{LAI}_2}{2}\right) \times \text{Time Interval}$$
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| Leaf Area Ratio (LAR) |
$$\text{LAR} = \frac{\text{Leaf Area}}{\text{Plant Dry Weight}}$$
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| Specific Leaf Area (SLA) |
$$\text{SLA} = \frac{\text{Leaf Area}}{\text{Leaf Dry Weight}}$$
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| Specific Leaf Weight (SLW) |
$$\text{SLW} = \frac{\text{Leaf Dry Weight}}{\text{Leaf Area}}$$
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| Crop Growth Efficiency (CGE) |
$$\text{CGE} = \frac{\text{Economic Yield}}{\text{Biological Yield}}$$
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