Methodology: Formulas, Sources and Testing
The formula, source, assumptions and tests behind every calculator on this site.
This page documents every formula the calculators use, where it comes from, and how it is tested. All calculation runs in your browser in plain JavaScript.
Effort, capacity and duration
E = people × hours per day × availability ÷ 100 duration = ⌈ effort × (1 + buffer ÷ 100) ÷ E ⌉
This is the standard relationship between effort (work) and duration (elapsed time) used in project estimation: duration equals effort divided by the resources applied. The ceiling reflects that a partly used day is still a day. The calendar finish date counts working days forward from the start date, skipping non-working weekdays and the holidays you supply. The start date counts as day 1 when it is a working day.
Team size for a deadline
people = ⌈ effort × (1 + buffer ÷ 100) ÷ (days × hours per day × availability ÷ 100) ⌉
PERT
TE = (O + 4M + P) ÷ 6 σ = (P − O) ÷ 6 σpath = √Σσ² z = (D − ΣTE) ÷ σpath
The three-point estimate comes from the Program Evaluation and Review Technique, first described by Malcolm, Roseboom, Clark and Fazar, "Application of a Technique for Research and Development Program Evaluation", Operations Research 7(5), 1959. The 1-4-1 weighting and the (P − O) ÷ 6 standard deviation are the classic PERT approximations of a beta distribution. Summing variances for independent tasks and treating the total as normal is the usual large-path approximation.
Two kinds of interval are shown, and they use different z-values on purpose. A two-sided range (TE ± zσ) uses z = 1.282, 1.645 and 1.960 for 80%, 90% and 95%. A one-sided "finish by" duration (TE + zσ) uses z = 0.8416, 1.2816 and 1.6449, because all of the stated confidence sits below the deadline.
The normal cumulative distribution is computed from the error function using the polynomial approximation 7.1.26 in Abramowitz and Stegun, Handbook of Mathematical Functions (1964), whose maximum error in erf is 1.5 × 10-7.
Critical path method
ES = max(EF of predecessors) EF = ES + d LF = min(LS of successors) LS = LF − d total float = LS − ES
The forward and backward pass method was developed in the late 1950s; see Kelley and Walker, "Critical-Path Planning and Scheduling", Proceedings of the Eastern Joint Computer Conference, 1959. The calculator supports finish-to-start links only, detects cycles with a topological sort, and treats tasks with zero total float as critical. Free float is the smallest successor ES minus the task's EF.
Hours and days
days = hours ÷ hours per day weeks = days ÷ days per week
Testing
The site has an automated test suite that exercises every formula above, including edge cases such as cycles, zero variance, floating-point rounding, weekends and holidays. The numbers in each page's worked examples are asserted in those tests, and a page does not ship until its examples match the tool's output.
General assumptions
- Inputs are exact numbers you supply. The calculators do not estimate effort for you.
- Results are planning aids, not guarantees. Use them with judgement.
Found an error? See the contact page.
Last updated 19 October 2026. Reviewed by Umesh Manral. Business Analyst, Excel VBA automation expert and web application developer who built this site to track daily project tasks.