Grouping Factor Calculator

Are you trying to figure out how much efficiency is lost when individual units are placed in groups, like piles in a foundation or machines working together? It can be tricky to calculate the effect of grouping, since performance rarely scales linearly.

That’s why we built this simple Grouping Factor Calculator. In this article, you’ll not only get a free tool to calculate grouping efficiency instantly, but you’ll also learn the formula behind it and how it applies in real projects.

By the end of this page, you’ll be able to confidently calculate grouping factors and make informed engineering or project decisions.

How to Use This Calculator:

1. Enter N: The number of units in a row (e.g., number of piles in one line).
2. Input M: The number of rows of units (e.g., rows of piles).
3. Add pile details: Enter the pile diameter (d) and spacing (s).
4. Click "Calculate": Your result, the Grouping Factor and Group Capacity, will be displayed instantly.

The Formula Explained: How It All Works

For those who like to see the math behind the calculation, here’s the formula our calculator uses.

Grouping Factor = Eg / (N × Ei)

Where:

• Grouping Factor: The efficiency of the group (dimensionless, between 0 and 1).
• Eg: Total capacity of the group.
• N: Number of units.
• Ei: Capacity of a single unit.

A more practical approach in geotechnical engineering is the Converse-Labarre Formula for piles:

Grouping Factor = 1 − [((N − 1) × M + (M − 1) × N) / (N × M)] × (θ / 90)

Where:

• N = Number of piles in a row
• M = Number of rows
• θ = arctan(d/s), with d = pile diameter and s = pile spacing

Once Grouping Factor is found:

Group Capacity = Grouping Factor × (N × M) × Individual Pile Capacity

Practical Example: Let's Walk Through It

Let’s imagine you want to calculate the efficiency of a pile group for a small foundation project.

Scenario Data:

• N = 3 piles in a row
• M = 3 rows
• d = 0.3 m (pile diameter)
• s = 0.9 m (spacing)
• Individual pile capacity = 200 kN

Step 1: Calculate θ

θ = arctan(d/s) = arctan(0.3 / 0.9) = arctan(0.333) ≈ 18.43°

Step 2: Apply Converse-Labarre formula

Grouping Factor = 1 − [((3 − 1) × 3 + (3 − 1) × 3) / (3 × 3)] × (18.43 / 90)
= 1 − [(6 + 6) / 9] × 0.2048
= 1 − (12/9) × 0.2048
= 1 − 0.2731
= 0.727

Step 3: Group Capacity

Group Capacity = 0.727 × (3 × 3) × 200 = 0.727 × 1800 = 1308.6 kN

The Result: The group efficiency is 0.727 (about 72.7%), and the group capacity is 1308.6 kN. This means the piles lose some efficiency when grouped closely.

Grouping Factor Reference Table

Grouping Factor Range	Interpretation
0.9 – 1.0	Very efficient group
0.7 – 0.9	Moderate efficiency
0.5 – 0.7	Significant efficiency loss
<0.5	Poor grouping efficiency

Helpful Tips & Tricks

1. Larger spacing between units increases grouping efficiency by reducing interference.
2. Always use realistic spacing-to-diameter ratios for reliable results.
3. Use this calculator for quick checks, but rely on detailed geotechnical design for major projects.

FAQs