Scale
Before asking if a number is exactly right, ask if it’s roughly right. Most errors are 10x, not 10%.
The sanity check
A team presents a business case: £2m investment, £800k annual return, 40% ROI.
Before digging into assumptions, ask: is £800k plausible?
The product serves 50 customers paying £20k each — £1m total revenue. After costs, £800k profit would require 80% margins. For a services business, that’s impossible. For software with existing infrastructure, it might be reasonable. For a new product requiring dedicated support, it’s optimistic.
The calculation might be internally consistent. But if £800k can’t physically emerge from 50 × £20k, the spreadsheet is fiction.
Fermi estimation
Enrico Fermi famously estimated the yield of the first nuclear test by dropping scraps of paper and measuring how far the blast moved them. He was within a factor of 2 — close enough to be useful, from almost no data.
The technique: break a problem into components you can estimate, multiply rough guesses, and accept that being within 2-3x is often good enough.
Example: How many plumbers work in London?
- London population: ~9 million
- Households: ~3.5 million (rough average of 2.5 people per household)
- Plumber visits per household per year: maybe 0.5 (every other year on average)
- Visits per plumber per day: maybe 3-4
- Working days per year: ~250
So: 3.5m × 0.5 = 1.75m visits annually. 1.75m ÷ 250 days = 7,000 visits per day. 7,000 ÷ 3.5 visits per plumber = 2,000 plumbers.
Is that exactly right? No. Is it roughly right — closer to 2,000 than to 200 or 20,000? Almost certainly.
The value isn’t precision. It’s having a baseline to compare against claims. If someone says “there are 50,000 plumbers in London,” you can say: that seems high by 10x, show me the maths.
Spotting errors
Most serious errors aren’t small — they’re orders of magnitude wrong.
Decimal place errors. £200k becomes £2m or £20k. These are obvious if you have order-of-magnitude intuition, invisible if you’re just checking whether the spreadsheet formulas work.
Unit confusion. Monthly figures treated as annual. Per-customer figures treated as totals. Thousands confused with millions. The number is “correct” in the wrong unit.
Missing scale factors. A cost per unit multiplied by the wrong volume. A rate applied to the wrong base. The calculation is right; the inputs are mismatched.
Implausible outputs. A margin that exceeds 100%. A growth rate that would make the company larger than its market. A headcount productivity that would require each person to work 200 hours per week.
The defence isn’t checking every cell. It’s asking: does the answer make sense given what I know about the world?
Building intuition
Order-of-magnitude intuition comes from accumulating reference points.
Revenue per employee. Software companies: £200-500k. Professional services: £100-200k. Retail: £50-150k. Manufacturing: varies wildly by automation level. If someone quotes £1m revenue per employee for a consulting firm, something is off.
Gross margins. Software: 70-85%. Professional services: 30-50%. Distribution: 15-25%. Retail: 25-40%. A “software” company with 40% gross margin isn’t really software — it’s services dressed up.
Customer acquisition payback. Healthy SaaS: 12-18 months. Aggressive growth mode: 18-24 months. Unsustainable: 30+ months. A business claiming 6-month payback on enterprise customers is probably miscalculating.
Growth versus market. If the total market is £500m and the company projects £200m revenue in five years, they’re claiming 40% market share. Possible, but requires extraordinary execution or a flawed market sizing.
These baselines don’t tell you if a number is right. They tell you if it’s in the right neighbourhood — or wildly outside it.
The practice
Estimate before you calculate. Before opening the spreadsheet, guess what the answer should be. If the calculated answer differs by 10x, either your intuition is wrong or the calculation is.
Triangulate with different methods. Estimate the market size top-down (population × penetration × price) and bottom-up (known customers × expansion potential). If they’re wildly different, investigate.
Know your reference points. For your industry, know the typical ratios: margins, productivity, growth rates, retention. When a number departs from typical by more than 2x, ask why.
Ask “is this physically possible?” £10m revenue from 100 customers requires £100k average. Is that plausible for the product? £50m from a 10-person team requires £5m per person. Is that achievable?
Precision is overrated. A number that’s right to two decimal places but wrong by a factor of ten is worthless. Get the order of magnitude right first. Refinement can come later.
Connects to Library: Base Rates — Start with what usually happens before refining the specifics.