Practising six versions of “population times penetration” will make that equation feel familiar. It will do less for you when the interviewer asks how many containers a service needs or how much power a backup system must deliver.
Use these six exercises to practise choosing the unit before choosing the numbers. Each has one main trap. Write the equation first, calculate, then explain what the answer lets the client decide.
All figures below are fictional teaching inputs. The value of the exercise is in the reasoning, so give yourself a clean sheet rather than reading the solution while calculating.
1. Annual appliance replacements
A city has 800,000 residents and 2.5 residents per home. Half its homes fall within an installer’s target segment. Eight per cent of those homes replace their heating system this year; 25% of replacement customers choose the installer’s technology.
Question: How many installations does that create this year?
There are 320,000 homes, of which 160,000 are in scope. Annual replacement decisions are 160,000 × 8% = 12,800. The technology captures 12,800 × 25% = 3,200 installations.
The target housing base is 160,000, but the annual market is 3,200. The replacement rate converts homes that exist into purchases occurring this year.
Decision sentence: “The annual market is about 3,200 installations, so I would compare that with delivery capacity before adding crews.”
If the interviewer adds a separate early-upgrade programme, apply it to homes not already counted in this year’s replacement decisions. Translate the resulting installations into installer hours before estimating the hiring need.
Quick Guesstimate Drill
A tyre-fitting chain is deciding whether a new depot serving local parcel-delivery vans would have enough work to justify two fitting bays.
- Delivery vans in region
- 6,000
- Tyres per van
- 4
- Average tyre life
- 2 years
How many van tyres will need replacing in the region each year?
2. Broadband connections and launch revenue
A district has 18,000 homes. The provider covers 70%, and 25% of covered homes are expected to connect during the first year. Assume all covered homes qualify for the offer.
Question: How many year-end connections are expected, and what is the annual revenue run rate at £40 per month?
Covered homes are 18,000 × 70% = 12,600. Expected connections are 12,600 × 25% = 3,150. The year-end annualised revenue is 3,150 × £40 × 12 = £1.512 million.
That revenue is a run rate. If the customers connect gradually, they do not all pay for twelve months in the launch year. You need the activation schedule to estimate revenue actually earned.
Decision sentence: “The plan reaches 3,150 subscriptions, but I would use the connection ramp to estimate first-year cash inflow.”
The distinction between coverage and take-up is also visible in Ofcom’s infrastructure reporting. Calculate covered households first, then apply take-up only to households that can receive the service.
3. Lounge visits without overlapping groups
A terminal has 15,000 departures per day. Twelve per cent are premium-ticket travellers, and half of them visit the lounge. A separate group of non-premium eligible members represents 10% of departures, with 30% visiting.
Question: What is daily lounge demand?
Premium travellers generate 15,000 × 12% × 50% = 900 visits. Non-premium members generate 15,000 × 10% × 30% = 450. Total demand is 1,350 visits per day.
The word “separate” matters. If the membership figure included premium travellers, you would need to remove overlap before adding the groups.
Decision sentence: “Daily demand is about 1,350 visits; seat requirements depend on visit duration and how those arrivals cluster around departures.”
A daily total cannot tell you the busiest hour’s occupancy. Estimate peak-hour arrivals and multiply by average dwell time to test the lounge’s space requirement.
4. A reusable container fleet
A service issues 1,500 containers per day. Each takes four days to complete the whole return-and-cleaning cycle. The operator wants a 25% buffer above the average circulating requirement.
Question: How many containers should the initial fleet contain?
The circulating requirement is 1,500 × 4 = 6,000 containers. Adding the buffer gives 6,000 × 1.25 = 7,500.
If the cycle falls to three days, the fleet requirement falls to 1,500 × 3 × 1.25 = 5,625, freeing 1,875 containers. That is a stock reduction, not an annual reduction in uses.
Decision sentence: “We need 7,500 containers at the current cycle time; faster returns could reduce the initial purchase, subject to the cost of achieving them.”
Add washing capacity, loss rates and the cost of faster collection before recommending a fleet size.
5. Backup power and duration
A site needs to protect 4 MW of constant load for 90 minutes. The exercise requires 25% power headroom, sustained for the whole period.
Question: What power output and delivered energy are required?
Planned power is 4 × 1.25 = 5 MW. Ninety minutes is 1.5 hours, so energy is 5 × 1.5 = 7.5 MWh.
A 4 MW system with 10 MWh fails the power requirement. A 6 MW system with 6 MWh fails the duration requirement. Check both dimensions against the service.
Decision sentence: “The requirement is 5 MW for 90 minutes, or 7.5 MWh delivered; I would compare supplier ratings at that same delivery boundary.”
Divide required usable energy by the battery’s usable fraction and conversion efficiency to estimate purchased capacity.
Quick Guesstimate Drill
A parcel hub is choosing a sorting plan. Most parcels arrive after the evening collection rounds, so the busy period matters as much as the daily total.
- Parcels per day
- 12,000
- Share in evening window
- 40%
- Evening window length
- 2 hours
| Plan | Peak rate (parcels per hour) | Daily capacity (parcels) |
|---|---|---|
| A | 3,000 | 10,000 |
| B | 2,000 | 16,000 |
| C | 2,500 | 14,000 |
Which plan can handle both the evening peak and the full day?
6. AI traffic during the busy hour
An assistant has 40,000 daily active users making five requests each. Twenty per cent of those requests arrive within the busiest hour.
Question: What is the average request rate during that hour?
Daily traffic is 200,000 requests. The busy hour contains 40,000, giving 40,000 ÷ 3,600 ≈ 11.1 requests per second.
That is the average within the busy hour. To size serving capacity, you still need a burst assumption, the work each request creates and measured performance under that workload.
Decision sentence: “The busy-hour average is roughly eleven requests per second; the capacity target should reflect bursts and the actual request mix.”
For AI requests, include retries and output length, then use response time to estimate the concurrent requests at the peak.
Review the mistake, then choose another exercise
Check the point at which your reasoning went wrong. If you confused homes with annual purchases, practise stock-to-flow conversions. If you got the correct number but gave no implication, repeat only the final explanation. If your groups overlapped, redraw the segmentation before doing more arithmetic.
Name the one input you would investigate first and the evidence that could replace its assumption. Writing the equation is only part of making the estimate useful.
Return to the market-sizing guide if choosing the equation remains the hardest step. Then take one worked example, change a single assumption and explain whether the recommendation changes.
Frequently asked questions
Choosing the right unit
Why isn't population times penetration enough for market sizing?
Many sizing questions are not about how many people buy. A fleet question needs the daily issue rate multiplied by the cycle time. A backup power question needs power and duration. Choose the unit before you choose any numbers, and write the equation first. Then calculate and explain what the answer lets the client decide.
How do I get from residents to annual installations?
Convert people into homes, then homes into decisions made this year. 800,000 residents at 2.5 per home gives 320,000 homes, of which 160,000 are in the target segment. Eight per cent replace their heating this year, which gives 12,800 decisions. The installer wins 25%, so 3,200 installations. The trap is treating the number of homes as this year's purchases.
Is an annual run rate the same as first-year revenue?
No. In the article's example, 3,150 year-end connections at £40 a month give a run rate of about £1.51 million a year. If homes connect gradually, revenue earned during the first year will be lower, because the early months have fewer paying customers. Say clearly which of the two figures you are giving.
How do I avoid double counting when I add customer segments?
Check that the groups do not overlap before you add them. In the lounge example, premium travellers produce 900 visits and a separate group of non-premium members produces 450, for a total of 1,350. If the member group also included premium travellers, adding the two would count some people twice. Redraw the segments whenever overlap is possible.
Fleets, power and peak demand
How many reusable containers does a service need?
Multiply daily issues by the number of days each container spends in the cycle, then add the buffer. At 1,500 a day and a four-day return and cleaning cycle, 6,000 containers circulate. A 25% buffer brings the fleet to 7,500. The trap is sizing the fleet to daily issues alone, which ignores the days each container is unavailable.
What happens to the fleet if the cycle gets faster?
The fleet shrinks in proportion. A three-day cycle needs 4,500 circulating containers, or 5,625 with the same 25% buffer. That is 1,875 fewer than the four-day plan. So cycle time is a commercial lever. Faster returns or cleaning reduce the money tied up in containers, which is a useful implication to point out.
What is the difference between power and energy in a backup question?
Power is how much the system delivers at any moment. Energy is power multiplied by time. The site needs 5 MW, which is 4 MW plus 25% headroom, for 1.5 hours, so 7.5 MWh. A 4 MW system with 10 MWh still fails, because it cannot meet the power requirement no matter how much energy it stores.
Does the headroom apply to power or to energy?
In this exercise, the 25% headroom applies to power and must hold for the whole 90 minutes. Energy then follows from the higher power figure: 5 MW for 1.5 hours. Read the requirement carefully. Applying headroom only to energy, or only for part of the period, would understate what the system must deliver.
How do I estimate requests per second for an AI assistant?
Start with daily requests, isolate the busy hour, then divide by the number of seconds in it. 40,000 users making five requests each gives 200,000 a day. Twenty per cent arrive in the busiest hour, which is 40,000, or about 11.1 requests per second. Converting to a per-second figure makes it usable for capacity decisions.
Is the busy-hour average enough to size servers?
Not on its own. The 11.1 figure is an average across the busy hour, and requests will not arrive evenly within it. To size serving capacity, you still need to account for how traffic varies inside that hour. Say this explicitly rather than presenting the average as the capacity requirement.
Reviewing and explaining your estimate
What should I do after getting a sizing question wrong?
Find the exact step where your reasoning went wrong and practise that skill, not the whole case. If you confused homes with annual purchases, practise converting stocks into flows. If your groups overlapped, redraw the segments before doing more arithmetic. If the number was right but you gave no implication, practise only the final explanation.
How do I finish a market-sizing answer well?
Say what the number lets the client decide. Then name the one input you would investigate first and the evidence that could replace that assumption. In the installer example, that could be the 8% annual replacement rate, since the whole estimate depends on it. This shows the interviewer you know which assumption matters most.