The prevalence of cost overrun in project delivery suggests an acute dearth of inclusive understanding of the effect of risks on construction cost estimation. In aberrant to the generic assumptions, customary to inquiries in construction risk researches, this paper appraised critical construction estimating risks. The study evaluated the sources, frequency and significance of construction estimating risks, using data from a questionnaire survey of 206 quantity surveyors in Nigeria. The data were analysed using factor analysis, Fussy Set Theory, Terrell Transformation Index (TTI), and Kruskal Wallis H tests. The results showed that estimating risks are correlate seven principal sources, namely: estimating resources, construction knowledge, design information, economic condition, the expertise of estimator, geographic factor, cost data, and project factors (λ, > 0.70 <1.0). Twenty-nine risk factors likewise emerged critical construction estimation risks (TTI, 69-87 > 65 percent) and the top three were low construction knowledge, inaccurate cost information and changes in government regulations (factor scores > 0.60 > 0.50). The awareness and accurate assessment of these risks into project cost estimation would reduce cost overrun. The study, therefore, recommends synergies between projects’ internal/ external environments for proper scoping of these risks into project estimates.