Coffee shop queue and counter calculator
Enter your busiest hour's orders and how long each order and drink takes for the line and pick-up crowd to make room for.
Counter and queue planner
Your busiest hour: how many orders, how long each takes at the till and at the machine. The starting values are an example; time your own.
The line to plan for
Plan for 7 people in line8.5 m (28 ft) of line at LOS C, with the person ordering
- Tills busy
- 60 orders × 45 s ÷ (1 × 3,600 s) = 75% · they take up to 80 orders an hour
- Orders that wait
- 75%, 2 min 15 s on average · 2.3 people waiting on average
- Line to plan for (90% of the time)
- (7 waiting + 1 ordering) × 3.5 ft = 8.5 m (28 ft) · longer than the 5.5 m
- Drink makers busy
- 60 × 1 drink × 50 s ÷ (1 × 3,600 s) = 83% · they make up to 72 drinks an hour
- Waiting at pick-up
- 5.0 people on average (an order waits 5 min 00 s for its drinks) · about 50 ft² (4.6 m²) at 10 ft² each
The line to plan for runs past the room you have: fold it back along a rail, add a till, or move tables out of its way. Where a line turns back around a rail end under 48 in wide, the turn needs 42 in (1,065 mm) lanes and 48 in (1,220 mm) at the turn.
At the counter: the order point and the pick-up each need a part at most 915 mm (36 in) high, either 915 mm (36 in) long with room to pull up alongside or 760 mm (30 in) long with knee and toe space, and the line itself is a walking route at least 915 mm (36 in) wide.
The arithmetic treats arrivals and service times as random (an M/M/c queue), which suits a busy hour; steadier service gives shorter lines than shown. The 90% line and making an order's drinks one after another are this tool's own choices.
Planning guidance, not a code or compliance check. Sources: queue arithmetic, Adan and Resing, M/M/c [1]; spacing in line, TCQSM Exhibit 10-32 [2]; counters and the line, 2010 ADA Standards §227, §403.5, §904.4 [3].
From the café floor plans guide, with an editable template, pictures and more figures.
METHOD
How the calculation works
The tills and the people making drinks are two queues in a row. Each is treated as an M/M/c queue: orders arrive at random at an average rate and take a random time to serve [1]. The line's length in floor comes from the spacing of people in a queue [2].
- How busy the tills are (ρ)
- orders an hour × seconds an order ÷ (tills × 3,600 s); at 100% or more the line grows without end
- Orders that wait (ΠW)
- the Erlang C formula for the number of tills and ρ, Adan and Resing (5.1)
- Average people waiting
- ΠW × ρ ÷ (1 − ρ), (5.2)
- Average wait
- ΠW ÷ (1 − ρ) × seconds an order ÷ tills, (5.3)
- Line to plan for
- the smallest n with ΠW × ρ^(n + 1) ≤ 10%: the line is n or shorter 90% of the time
- Line length
- (n + 1) × the roomier spacing of the chosen level of service: the people waiting and the person ordering at the till, who stands in the line's first place
- Waiting at pick-up
- orders with drinks a second × (average drink wait + the order's drinks × seconds a drink), by Little's law, an order's drinks made one after another (below one drink an order, that share of orders waits for one drink); floor at the level's roomier area a person
Worked example
The calculator's starting values: 60 orders an hour, 1 till at 45 s an order, 1 person making 1 drink an order at 50 s, level of service C and 5.5 m of room. They are an example, not published figures.
- Tills busy
- 60 × 45 ÷ 3,600 = 75%
- Orders that wait
- 75% (with one till, ΠW equals ρ)
- Average people waiting
- 75% × 75% ÷ 25% = 2.25
- Average wait
- 2 min 15 s
- Line to plan for
- (7 waiting + 1 ordering) × 3.5 ft = 8.5 m (28 ft) · longer than the 5.5 m of room
- Drink maker busy
- 60 × 1 × 50 ÷ 3,600 = 83%
- Waiting at pick-up
- 5.0 people (a one-drink order takes 5 min 00 s from order to hand-off) · about 50 ft² at 10 ft² each
Here the drink maker is busier than the till (83% against 75%), so the crowd at the pick-up is the thing to watch: at 100% busy the wait has no end. The 90% line and making an order's drinks one after another are this calculator's own choices.
FIGURES
The figures it uses
| Figure | Value | How the calculator uses it | Source |
|---|---|---|---|
| M/M/c formulas | (5.1) to (5.3) | Orders that wait, average people waiting and average wait at the tills and at the machine | Adan and Resing, ch. 5 [1] |
| Level of service B | 3.5–4.0 ft apart, 10–13 ft² a person | The line at the roomier spacing, the pick-up at the roomier area | TCQSM Exhibit 10-32 [2] |
| Level of service C | 3.0–3.5 ft apart, 7–10 ft² a person | The line at the roomier spacing, the pick-up at the roomier area | TCQSM Exhibit 10-32 [2] |
| Level of service D | 2.0–3.0 ft apart, 3–7 ft² a person | The line at the roomier spacing, the pick-up at the roomier area | TCQSM Exhibit 10-32 [2] |
| Accessible counter part | at most 915 mm (36 in) high; 915 mm (36 in) long alongside, or 760 mm (30 in) long with knee and toe space | Named for the order point and for the pick-up | 2010 ADA Standards §904.4.1, §904.4.2, §227.3 [3] |
| Width of the line | 915 mm (36 in) | The width the line is drawn at | 2010 ADA Standards §227.5, §403.5.1 [3] |
The queuing levels of service were written for transit platforms; this calculator applies them to a line at a counter.
A queue estimate from average timings is a first check for an early layout, not a staffing plan or an accessibility review. Time your own orders in a busy hour, and confirm the counter and its line with your building authority and a qualified professional.
QUESTIONS
Questions about this calculator
Where do I get the timings?
Time your own counter in a busy hour: the seconds from greeting a customer to taking payment, and from starting a drink to handing it over, averaged over a dozen or more. A new shop can time a rehearsal. The starting values are an example, not published figures.
Why is the line longer than the average?
Orders arrive in bursts. The calculator plans for the line the queue stays within 90% of the time, which is longer than the average number waiting; with one till at 75% busy the average is 2.3 people but the line to plan for is 7. [1]
Why does the line grow without end at 100% busy?
When orders arrive as fast as the tills can serve them or faster, every short gap in orders is lost for good while every burst adds to the line, so it never settles. The queue formulas only apply below 100%; at or above it the calculator says the line keeps growing and how many orders an hour the tills are short (none on average at exactly 100%, which still never settles). [1]
Which level of service should I pick?
The manual calls C to D or better the typical design level for waiting areas, and says D is not recommended for long waits. At C people stand 3.0 to 3.5 ft apart; pick B for a roomier line or for long waits. [2]
References
Sources of the figures this calculator uses.
- Queueing Systems (lecture notes), Chapter 5, M/M/c queueIvo Adan and Jacques Resing, Department of Mathematics and Computing Science, Eindhoven University of Technology, 2015. §5.1, the delay probability (5.1) and the equilibrium probabilities; §5.2, the mean queue length (5.2) and mean waiting time (5.3).
- Transit Capacity and Quality of Service Manual, Third Edition (TCRP Report 165), Chapter 10, Station CapacityTransportation Research Board, Transit Cooperative Research Program, 2013. Exhibit 10-5, Illustration of Queuing Area Level of Service (p. 10-14); Exhibit 10-32, Levels of Service for Queuing Areas (p. 10-55): average area per person and average spacing between people in a queue, LOS A to F, after Fruin.Written for transit platforms and waiting areas; this page applies its queuing figures to a line at a counter.
- 2010 ADA Standards for Accessible DesignU.S. Access Board. §226.1, dining surfaces (at least 5 percent of seating and standing spaces), §226.2 dispersion; §227.3 and its advisory, counters (order and pick-up both); §227.5, queues and waiting lines; §308.2.1, forward reach 15 to 48 in, and §904.5.1, self-service shelves and dispensers of food service lines; §403.5.1, walking surfaces 36 in (915 mm); §403.5.2, 180-degree turns; Advisory 902.1, bars and lunch counters are dining surfaces; §902.3, 28 to 34 in high; §904.4.1 and §904.4.2, sales and service counters.
Lay out the counter and line in the café template
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