A eyeball guesstimate is a often pejorative slang description of an estimate best described as a guess. The potential margin of error in such an estimate is probable ±30%.
Wikipedia describe a Guesstimate as:
Guesstimate is an informal English portmanteau of guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture.
PhilPaint (aka OutOfTheBucket.com)describes a Guesstimate as
The “eye-ball” method involves a visual inspection and then the computation of the estimate. This method relies almost exclusively on the experience of the estimator and is prone to numerous errors. Further, it is virtually impossible to teach to others, is inconsistent, and provides no means for detailed monitoring. While there are variations of this method, some being more complex than others, all are basically a “guesstimate”.
And in his 1981 book Professional Cost Estimating for Residential Remodeling, Renovation, Rehabilitation, and Repair Walter W Stoeppelwerth wrote:
Many old-timers in the business use this system, which is based on the estimator’s knowledge and experience without any calculations except very basic measurements, at most. By this method an addition would be figured by square feet, perhaps $70 per square foot for a frame addition and $90 per square foot for brick. Little if any thought is given to layout, access, special requirements or particular specifications.
Kitchens and baths are figured based on low, medium or high priced cabinets and appliances. Some jobs, such as aluminum siding, roofing, concrete or even storm windows, might not have any square footage or quantity figured at all, but the estimator would simply look at the house and name a selling price for the job.
In some parts of the country this method is known as the “wag” or “swag” system. A “wag” is a wild-ass guess, while the “swag” is a scientific wild-ass guess.