Enter Matrix Inputs
Use the controls below, then calculate the adjusted origin-destination matrix.
Example Data Table
This sample 4-zone matrix demonstrates how row totals, column totals, and the grand total are arranged.
| Origin \ Destination | Zone 1 | Zone 2 | Zone 3 | Zone 4 | Origin Total |
|---|---|---|---|---|---|
| Zone 1 | 0 | 120 | 80 | 60 | 260 |
| Zone 2 | 110 | 0 | 95 | 70 | 275 |
| Zone 3 | 75 | 90 | 0 | 85 | 250 |
| Zone 4 | 55 | 65 | 100 | 0 | 220 |
| Destination Total | 240 | 275 | 275 | 215 | 1,005 |
Formula Used
1. Adjusted Cell Flow
Fij,adj = Fij,obs × P × (1 + g / 100)
2. Origin Total
Oi = Σ Fij,adj
3. Destination Total
Dj = Σ Fij,adj
4. Grand Total
T = ΣΣ Fij,adj
5. Intra-zonal Total
I = Σ Fii,adj
6. Inter-zonal Total
E = Tall adjusted - I
7. Share Percentage
Share = (Zone Total ÷ Grand Total) × 100
8. Directional Imbalance Index
Imbalance = [Σ |Fij - Fji| ÷ Inter-zonal Total] × 100
Here, P is the peak or scaling factor, and g is the growth percentage.
How to Use This Calculator
- Choose the number of traffic zones you want to analyze.
- Enter a scenario name and select the traffic unit.
- Input the observed origin-destination values in the matrix.
- Set the growth factor and peak or scaling factor.
- Choose whether intra-zonal diagonal values should be included.
- Select the number of decimal places for displayed results.
- Press Calculate Matrix to generate totals and charts.
- Use the CSV or PDF buttons to export the result block.
Frequently Asked Questions
1. What does this calculator measure?
It evaluates origin-destination traffic movements, then calculates row totals, column totals, adjusted flows, inter-zonal movement, intra-zonal movement, and directional imbalance.
2. What is a traffic flow matrix?
A traffic flow matrix is a table showing trips from each origin zone to each destination zone. It helps engineers study movement structure across a network.
3. Why would I exclude diagonal values?
Diagonal cells represent trips that start and end in the same zone. Excluding them helps when you only want external network movement between different zones.
4. What does the growth factor do?
The growth factor increases or reduces observed flows by a percentage. It is useful for forecasting future conditions or testing scenario-based demand changes.
5. What is the peak or scaling factor?
This factor converts the observed matrix to another analysis level, such as peak-hour expansion, calibration adjustment, or scaled scenario comparison.
6. What does directional imbalance mean?
Directional imbalance shows how different one-way movements are from their reverse movements. Higher values suggest stronger directional asymmetry in the network.
7. Can I use decimal traffic values?
Yes. The matrix accepts decimal entries, which is useful for modeled demand, averaged observations, passenger car unit conversions, or balanced matrices.
8. What does the heatmap show?
The heatmap highlights large and small flows across all zone pairs. Darker or stronger cells reveal dominant movement paths and important corridor interactions.