Bottleneck Calculator
Find the station that limits the line and what the line can produce.
In short
Find the station that limits the line and what the line can produce.
Formula: Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity
What this calculator does
The minimum of the entered station capacities, with the position of that station reported. Optional stations left at zero are excluded rather than treated as stopped.
Use it to turn Station 1 capacity, Station 2 capacity, Station 3 capacity (optional), Station 4 capacity (optional), and the other shown inputs into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
Inputs and what they mean
- Station 1 capacity
- — number value.
- Station 2 capacity
- — number value.
- Station 3 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 4 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 5 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 6 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity.
Inputs used: Station 1 capacity, Station 2 capacity, Station 3 capacity (optional), Station 4 capacity (optional), Station 5 capacity (optional), Station 6 capacity (optional).
Edge handling: Station 1 capacity is required.; Station 1 capacity cannot be negative.; Station 1 capacity must be no more than 1000000000000.; Station 2 capacity is required.; Station 2 capacity cannot be negative..
Worked example
Six stations, one constraint
- Start with Station 1 capacity: 120, Station 2 capacity: 95, Station 3 capacity (optional): 140, Station 4 capacity (optional): 110, Station 5 capacity (optional): 0, Station 6 capacity (optional): 0.
- Apply the method: Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity.
- The line can only go as fast as its slowest station, whatever the others can do.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this bottleneck calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: Massachusetts Institute of Technology — 2.854 Introduction to Manufacturing Systems
Last reviewed:
Common questions
Where does this formula come from?
MIT OpenCourseWare 2.854 Introduction to Manufacturing Systems — throughput is output per unit of time, cycle time is run time divided by the units produced, line capacity is set by the slowest station, and balance efficiency compares total work content with the number of stations multiplied by the longest station time. See the source link on this page.
What kind of calculation is this?
The slowest station sets the capacity of the whole line, whatever the other stations can do. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
Arithmetic over the figures entered — it cannot tell whether the measurements behind them are right. A measured result, an industry benchmark and an organisation's target are three different things; only the entered figures are used. A single sequential line is assumed. Parallel paths, shared resources and large buffers change where the constraint sits.
How do I use the Bottleneck Calculator?
Enter the required values for Station 1 capacity, Station 2 capacity, Station 3 capacity (optional), Station 4 capacity (optional), Station 5 capacity (optional), and the other fields shown. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Bottleneck Calculator use?
Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the Bottleneck Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Formula, source and verification
The slowest station sets the capacity of the whole line, whatever the other stations can do.
The question it answers: Which station is holding the line back, and how evenly is the work spread across the stations?
The formula
Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity
- ci — Station capacity
- (count). Units per hour each station can produce; stations left at zero are not counted.
- Cmin — Line capacity
- (count). The smallest entered station capacity.
- Cmax — Fastest station
- (count). The largest entered station capacity.
Units: Units per hour in and out.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
The minimum of the entered station capacities, with the position of that station reported. Optional stations left at zero are excluded rather than treated as stopped.
Assumptions built into the result
- Mathematical: Every quantity, time and rate is the figure the user entered, measured over the period they describe.
- Mathematical: Times and counts refer to the same period and the same resource.
- Mathematical: Stations run in sequence with no parallel routing and no buffer large enough to break the constraint.
Figures this calculator will never guess for you
- No industry benchmark, target utilisation or target availability is supplied or applied.
- No shift length, break allowance, downtime allowance or standard rate is assumed.
- Optional components are excluded from the result when left at zero.
Limitations
- Arithmetic over the figures entered — it cannot tell whether the measurements behind them are right.
- A measured result, an industry benchmark and an organisation's target are three different things; only the entered figures are used.
- A single sequential line is assumed. Parallel paths, shared resources and large buffers change where the constraint sits.
Source and version
- Standard or reference
- Manufacturing systems — throughput, cycle time, work in process and line balancing — MIT OpenCourseWare (MIT OpenCourseWare 2.854 Introduction to Manufacturing Systems — throughput is output per unit of time, cycle time is run time divided by the units produced, line capacity is set by the slowest station, and balance efficiency compares total work content with the number of stations multiplied by the longest station time.)
- Published source
- Massachusetts Institute of Technology — Fall 2016
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Academic
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
Cite this page
Free Calculator. (2026, September 16). Bottleneck Calculator. https://freecalculator.tech/tools/bottleneck-calculator
"Bottleneck Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/bottleneck-calculator.
Bottleneck Calculator — Free Calculator, https://freecalculator.tech/tools/bottleneck-calculator
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