What each number is
Offered load, service level and speed of answer are arithmetic from the Erlang C queueing model on your inputs. That adherence equals the share of agents on the queue is a model assumption. The overtime cost is a conditional forecast at your hourly rate, multiplier, open hours and days.
Formulas
Calls per hour × AHT in seconds ÷ 3,600
In Erlangs: the agents busy every moment if calls arrived evenly.
Agents scheduled × adherence, rounded
Adherence taken as the share of scheduled agents available at any moment.
The probability a call waits, through the Erlang B recurrence B(n) = A × B(n−1) ÷ (n + A × B(n−1)), then C = n × B ÷ (n − A × (1 − B))
The same form the Staffing Calculator uses. It stays finite at any size.
1 − C × e^(−(agents − load) × answer-within seconds ÷ AHT)
The share answered within the target time. Zero when agents do not exceed the load.
C × AHT ÷ (agents − load)
The average wait across all calls.
The fewest agents on the queue that meet the target ÷ adherence, rounded up
Any agents beyond the roster are the gap.
Agents beyond the roster × open hours a day × open days a year × hourly rate × overtime multiplier
Assumes the call rate holds across the open hours; peaks need interval staffing.
Rules and bands
The agents on the queue answer the target share within the target time.
Scheduling more agents, or recovering adherence, is needed to hold the target.
The only line is your own target. The tool grades nothing else.
Every constant and where it comes from
Prices the overtime hours it takes to hold the service level target when adherence falls. Source: US Fair Labor Standards Act, 29 U.S.C. 207(a): overtime beyond 40 hours in a workweek is paid at not less than one and one half times the regular rate. A legal minimum; contracts, other jurisdictions and state law can set more.
The one agent wage benchmark the platform cites. Staffing, Cost per Contact and Channel Shift read it. It is the occupation median, no figure of the user's own, so a driver still at it grades evidence Directional. Source: US Bureau of Labor Statistics, Occupational Employment and Wage Statistics, May 2025 (released 15 May 2026), SOC 43-4051 Customer Service Representatives, national median hourly wage.
Worked example
Computed by the tool's own engine at its default inputs, so this page and the calculator always agree.
Agents scheduled: 100
Adherence: 92%
Calls per hour: 820
AHT: 360 seconds
Target: 80% within 20 seconds
Hourly rate: $21.53 (BLS median)
Overtime: 1.5x, 8 hours a day, 250 days
820 × 360 ÷ 3,600 = 82 Erlangs
100 × 92% = 92 on the queue: service level 88.5%, speed of answer 7s, target met
90 agents on the queue meet 80% within 20 seconds
89% adherence: 89 on the queue, service level 76.7%
90 ÷ 89% = 101.12, rounded up to 102, 2 beyond the roster
2 × 8 × 250 × $21.53 × 1.5 = $129,180 a year
10 Erlangs on 11, 12, 13 and 14 agents: 0.6821, 0.4494, 0.2853, 0.1741, the values in published Erlang C tables
Checked against
Cases whose answer is known outside this site. The test suite computes each one with this tool's own engine on every change.
Offered load 10 Erlangs on 11, 12, 13 and 14 agents. Result: 0.6821, 0.4494, 0.2853 and 0.1741. Erlang C formula (A. K. Erlang, 1917), as tabulated in standard Erlang C probability-of-wait tables.
Offered load 1 Erlang on 2 agents. The formula gives (1²/2! × 2/(2 − 1)) ÷ (1 + 1 + 1²/2! × 2/(2 − 1)) = 1 ÷ 3. Result: 0.3333. Erlang C formula (A. K. Erlang, 1917).
What this tool cannot tell you
- Adherence rarely falls evenly across the day. A miss concentrated in the peak costs more service level than the same average.
- Erlang C assumes callers wait until answered. With abandonment, measured service level runs higher than it predicts.
- Overtime assumes one call rate all day. Use interval staffing for peaks, which the Staffing Calculator sizes.
- The overtime cost is a conditional forecast. Hiring, cross-skilling or schedule changes can hold the target instead.