FREE TOOL
Line Balancing Calculator
Enter your takt time, or available time and demand, plus the work time at each station. Get the theoretical minimum number of stations, balance efficiency, balance delay, smoothness index, and which stations run over takt.
Line balancing calculator
| Station | Work time | Load vs takt |
|---|---|---|
| Station 1 | 52 s | 86.7% |
| Station 2 | 60 s | 100.0% |
| Station 3 | 45 s | 75.0% |
| Station 4 | 58 s | 96.7% |
| Step | Formula | Value |
|---|---|---|
| Takt time | Takt = (480 − 30) min × 60 / 450 | 60 s |
| Total work content | ΣTᵢ = 52 + 60 + 45 + 58 | 215 s |
| Theoretical minimum stations | Nmin = ⌈ΣTᵢ / takt⌉ = ⌈215 / 60⌉ | 4 |
| Bottleneck station time | Tmax = max(Tᵢ) | 60 s |
| Balance efficiency | Eb = ΣTᵢ / (n × Tmax) = 215 / (4 × 60) | 89.58 % |
| Balance delay | d = 1 − Eb | 10.42 % |
| Efficiency against takt | ΣTᵢ / (n × takt) = 215 / (4 × 60) | 89.58 % |
| Smoothness index | SI = √Σ(Tmax − Tᵢ)² | 17.12 |
| Output rate | 3600 / Tmax = 3600 / 60 | 60 units/h |
Formulas used
- Takt time
- Takt = (available time − breaks) / demand
- Total work content
- ΣTᵢ = sum of all station times
- Theoretical minimum stations
- Nmin = ⌈ΣTᵢ / takt⌉
- Balance efficiency
- Eb = ΣTᵢ / (n × Tmax)
- Balance delay
- d = 1 − Eb
- Efficiency against takt
- ΣTᵢ / (n × takt)
- Smoothness index
- SI = √Σ(Tmax − Tᵢ)²
Assumptions and limits
- Station times are the work time per unit at each station, including walking and handling but not waiting.
- Each station has one operator and the line moves one unit at a time.
- Tmax, the slowest station, sets the actual cycle time and output rate of the line.
- Times are averages. Variation between cycles is not modelled; a station whose average is close to takt will still miss takt on some cycles.
- Precedence constraints between work elements are not checked. The calculator rates a balance you have already laid out.
Worked example
Example: a line runs a 480-minute shift with 30 minutes of breaks and must ship 450 units. Four stations take 52, 60, 45 and 58 seconds.
| Step | Formula | Value |
|---|---|---|
| Takt time | Takt = (480 − 30) min × 60 / 450 | 60 s |
| Total work content | ΣTᵢ = 52 + 60 + 45 + 58 | 215 s |
| Theoretical minimum stations | Nmin = ⌈ΣTᵢ / takt⌉ = ⌈215 / 60⌉ | 4 |
| Bottleneck station time | Tmax = max(Tᵢ) | 60 s |
| Balance efficiency | Eb = ΣTᵢ / (n × Tmax) = 215 / (4 × 60) | 89.58 % |
| Balance delay | d = 1 − Eb | 10.42 % |
| Efficiency against takt | ΣTᵢ / (n × takt) = 215 / (4 × 60) | 89.58 % |
| Smoothness index | SI = √Σ(Tmax − Tᵢ)² | 17.12 |
| Output rate | 3600 / Tmax = 3600 / 60 | 60 units/h |
Result: Takt is 60 s, the theoretical minimum is 4 stations, balance efficiency is 89.6%, and station 2 is the bottleneck.
How to balance a production line
Start from takt time
Takt time is the pace demand requires. Every station's work time should be at or below it. The takt time calculator works this out from available time and demand; this calculator does the same step and then checks each station against it.
Read balance efficiency and balance delay
Balance efficiency compares the work actually done with the time paid for: n stations each waiting for the slowest one. Balance delay is the idle share. A line at 90% balance efficiency has 10% of its station time spent waiting.
Fix the bottleneck first
The slowest station sets output. Move work elements from it to the stations with the most slack, respecting the order the work must happen in, then recalculate. A lower smoothness index means the stations are closer to equal.
Write the new balance down
Once the balance works, record which work elements belong to each station on a standardized work combination sheet. Without it, the line drifts back to the old balance within a few shifts.
Common mistakes
- Balancing to the current bottleneck instead of takt. If the bottleneck is already over takt, an even balance still misses demand.
- Using one timed cycle per station. Time several cycles and use a representative value. Single readings hide variation.
- Ignoring precedence. A balance that moves a task before the step it depends on looks good on paper and fails on the floor.
- Loading stations to exactly 100% of takt. With normal variation, a station at takt will miss on some cycles. Leave some margin.
- Counting fractional stations. The minimum is always rounded up. 3.2 stations of work needs 4 stations.
Frequently asked questions
How do you calculate line balancing efficiency?
Divide total work content by the number of stations times the longest station time: Eb = ΣTᵢ / (n × Tmax). Four stations totalling 215 s with a slowest station of 60 s give 215 / 240 = 89.6%.
How many workstations do I need?
The theoretical minimum is total work content divided by takt time, rounded up. Real lines often need more because tasks can't be split freely.
What is the difference between balance efficiency and efficiency against takt?
Balance efficiency uses the slowest station, so it measures how evenly work is spread. Efficiency against takt uses takt time, so it also shows unused capacity when the whole line runs faster than demand.
What is the smoothness index?
The square root of the summed squared differences between the slowest station and each station. Zero means every station has the same load.
How is this different from the takt time calculator?
The takt time calculator gives takt and a stations-needed estimate from one total cycle time. This calculator takes the time at each station and rates the balance between them.
Sources
- Groover, M. P., Automation, Production Systems, and Computer-Integrated Manufacturing, Pearson — manual assembly lines: minimum workstations, balance efficiency and balance delay.
- Moodie, C. L. and Young, H. H., A Heuristic Method of Assembly Line Balancing for Assumptions of Constant or Variable Work Element Times, Journal of Industrial Engineering, 1965 — smoothness index.
- Rother, M. and Shook, J., Learning to See, Lean Enterprise Institute — takt time.
Results are computed in your browser from the published formulas named above. They are an engineering aid, not a substitute for the governing standard, your drawing, or your customer's requirements.