Cone of uncertainty: how wide should a quote be?
A project’s final cost can land from a quarter to four times your first estimate. How the range narrows by stage, and what to quote at each one.
Short answer Published ranges for software projects run from 0.25× to 4× your estimate at the idea stage down to 0.9× to 1.1× once detailed design is done. They narrow because decisions get made, not because time passes. The honest quote range depends on the stage you are actually at, and a fixed price offered early mostly prices what you do not yet know.
- Idea stage
- 0.25–4×of your estimate
- Requirements done
- 0.67–1.5×of your estimate
- Detailed design
- 0.9–1.1×of your estimate
- P80 cost, idea stage
- 1.94×in the $50,000 example
What the cone of uncertainty says
The cone of uncertainty describes how far a project’s final cost can sit from the estimate you made at each stage. Barry Boehm described the funnel in Software Engineering Economics (1981), and Steve McConnell later tabulated it as simple multipliers on effort and cost in Software Estimation: Demystifying the Black Art (2006). The numbers are the widely cited ones, and they are guidelines for software work, not laws of nature.
| Stage | What you have in hand | Final cost ÷ estimate | Low to high |
|---|---|---|---|
| Initial concept | A paragraph of intent, no agreed outcomes | 0.25× – 4× | 16× |
| Approved product definition | Agreed outcomes and a rough feature list | 0.5× – 2× | 4× |
| Requirements complete | Written, client-approved requirements | 0.67× – 1.5× | 2.25× |
| UI design complete | Approved screens or a working prototype | 0.8× – 1.25× | 1.56× |
| Detailed design complete | Technical design done, risky parts proven | 0.9× – 1.1× | 1.22× |
Read the first row as: if your estimate at the idea stage is $50,000, a final cost anywhere from $12,500 to $200,000 would not be surprising. The ranges are drawn so that 4× above and 0.25× below are mirror images, which is why the picture is usually shown on a log scale.
Figure 1. Final cost as a multiple of the estimate, by stage, on a log scale. The bars are the published ranges; the diamond is where the P80 cost lands in the worked example below.
At the idea stage the P80 is 1.94× the estimate. At detailed design it is 1.03×.
The cone narrows when you decide things
A common misreading is that the cone closes by itself as a project ages. It does not. The ranges are the best accuracy a given stage can support, and they only apply if the work that defines that stage has actually been done. One analysis of project data from a single software company, published in IEEE Software in 2006 (Todd Little), reported a spread of actual-to-estimate ratios that stayed roughly the same as projects progressed. Treat the exact multipliers as rough guides and the direction as the lesson.
What moves a project down the cone is a short list of decisions:
- Written, approved outcomes. A requirement the client has signed off on is worth more than three pages of notes.
- Proving the risky part first. A one-week prototype of the integration nobody has done before removes more uncertainty than a week spent refining everything else.
- Removing unknown dependencies. Access, data, third-party approvals and client availability widen the range until they are settled.
The cone also widens again. A material scope change sends you back up it, which is why a change should be re-estimated rather than absorbed; see a client budget below your quote for the negotiation side and pricing a change request for the arithmetic.
From a stage to a quote range
- Name your stage honestly. The usual mistake is treating a client’s one-page brief as “requirements complete”. Use the table above.
- Write the point estimate. The most likely cost to deliver, not the safest one.
- Apply the stage’s multipliers to get a low and a high, and keep your point estimate as the most likely value.
- Read the percentiles. The PERT calculator does this for one block of work; the simulation does it for a whole project.
- Quote at the percentile you use everywhere else, or quote a range and say which decisions would narrow it. The P50 versus P80 note covers choosing it.
A worked example: one $50,000 estimate at five stages
Take a project whose most likely cost to deliver is $50,000, priced to a 25% gross margin at P80 confidence (price = P80 cost ÷ 0.75). Only the width of the range changes between rows.
| Stage | Cost range | P50 | P80 | Minimum quote |
|---|---|---|---|---|
| Initial concept | $12,500 – $200,000 | $64,297 | $97,002 | $129,337 |
| Approved product definition | $25,000 – $100,000 | $53,136 | $66,591 | $88,789 |
| Requirements complete | $33,500 – $75,000 | $51,054 | $58,478 | $77,971 |
| UI design complete | $40,000 – $62,500 | $50,331 | $54,314 | $72,418 |
| Detailed design complete | $45,000 – $55,000 | $49,994 | $51,717 | $68,956 |
Inputs. Most likely cost $50,000 at every stage, so the table isolates the effect of range width; in real life the estimate itself moves as you learn. Optimistic and pessimistic values are the stage multipliers times $50,000. Beta-PERT (λ = 4), 100,000 runs, fixed seed. Illustrative figures, not market benchmarks. Figures are rounded for display, so recomputing from the rounded values can differ by a dollar or two.
At the idea stage the P80 cost is 1.94 times the estimate and the minimum quote is $129,337. At detailed design the same work quotes at $68,956. The $60,381 between them is what the lack of knowledge costs you to carry at the same risk policy.
Notice that the P50 is already above your estimate at the early stages. With a range that is lopsided towards overruns, the middle outcome sits higher than the most likely one, so a point estimate alone understates what a wide-stage project is likely to cost.
Figure 2. Minimum quote at P80 confidence and a 25% margin for the same $50,000 estimate. Blue is the quote you could give at the last stage; rust is the extra you must charge while you still do not know.
The extra falls from $60,381 at the idea stage to nothing at the last.
What narrowing is worth: the case for paid discovery
Moving from an approved product definition to completed requirements lowers the P80-based quote from $88,789 to $77,971, a drop of $10,818 (12%). If the discovery that gets you there costs the client less than that, they pay less in total and you have swapped a guess for a plan. Moving from the idea stage to an approved product definition is worth more still: $40,548 (31%).
Two cautions. The comparison holds the estimate fixed, and discovery may move it up or down; the real product of discovery is knowledge, and the price effect is a by-product. And a client who will not pay for discovery is telling you something about how much of the uncertainty they expect you to absorb.
What to offer when the client wants one number now
- Idea stage: an order-of-magnitude range, or a paid discovery. No fixed price.
- Product definition approved: a range, or a fixed price for the next phase only.
- Requirements complete: a fixed price at P80 with written assumptions and change control.
- UI or detailed design complete: a fixed price at the percentile you normally use.
If the client insists on a fixed price earlier than that, you have three honest options: price at the wide end and show them the premium, propose time and materials with a cap, or decline. Quoting a narrow price from a wide stage is the road to the fixed-price death spiral.
Using the stages in BidVariance
Enter your point estimate as the most likely value and the stage multipliers as the optimistic and pessimistic values. BidVariance treats the pessimistic value as a hard upper bound, so choose it deliberately: the top of the cone is a plausible high, not a guaranteed maximum.
The cone describes the whole project. If you apply the multipliers to every task and simulate, independent tasks partly cancel and the total range comes out narrower than the cone, for the reasons in why task P80s do not add up. To model project-level uncertainty, apply the stage range to the project total or add project-level risks for the shared causes. Free tools: the PERT calculator and the minimum bid price calculator; the full task network is in the app.
Frequently asked questions
What is the cone of uncertainty in project estimating?
It is the funnel of possible outcomes around an estimate: very wide at the idea stage and narrowing as requirements, design and risky work are settled. For software, published multipliers run from 0.25× to 4× of the estimate at the initial concept down to 0.9× to 1.1× at detailed design.
How accurate should a project estimate be at the requirements stage?
The published range for completed requirements is 0.67× to 1.5× of the estimate, about a 2.25 to 1 spread from low to high. Treat it as a guide: it assumes the requirements are written and approved, not just discussed.
Does the cone of uncertainty narrow on its own over time?
No. It narrows when decisions are made and risky work is proven. One analysis of project data from a software company reported a spread that stayed about the same as projects progressed, so the cone is the best accuracy a stage can support, not a promise.
Should I charge for a discovery phase before a fixed price?
When the stage is early and the client wants a fixed price, paid discovery is the cheapest way to narrow the range. In the worked example, moving from an approved product definition to completed requirements lowered the P80-based quote by $10,818, about 12%.
What optimistic and pessimistic values should I use for my stage?
Use the stage multipliers on your point estimate as a starting point, keep the point estimate as the most likely value, and adjust for what you actually know. In BidVariance the pessimistic value is a hard upper bound, so set it as a plausible high rather than a theoretical maximum.
Sources
- Boehm, B. W. (1981). Software Engineering Economics. Prentice-Hall.
- McConnell, S. (2006). Software Estimation: Demystifying the Black Art. Microsoft Press.
- Little, T. (2006). Schedule estimation and uncertainty surrounding the cone of uncertainty. IEEE Software, 23(3), 48–54.
- Cone of uncertainty, Wikipedia (overview and history).