Formula sheet
Construction Planning and Site Operations Formula Sheet
Construction formulas for readiness, CPM, float, PPC, productivity, bottlenecks, crane cycles, temporary works, maturity, earned value, RPN, and validation.
This formula sheet collects first-pass calculations used in construction planning and site operations. It is intended for work-package readiness, critical-path review, short-interval planning, site logistics, production control, temporary works, quality gates, commissioning, and handover validation.
The formulas do not replace the contract, approved schedule, temporary-works procedure, design standards, safety plan, inspection and test plan, or environmental permit. Use them to make field constraints explicit before work becomes unsafe, hidden, delayed, or difficult to correct.
How to Use This Formula Sheet
Use this formula sheet as a field decision aid, not as a substitute for the approved construction basis. Begin with the work package: identify the activity, location, predecessor work, drawings, permits, inspection hold points, crew, equipment, materials, temporary works, environmental controls, and handover requirement. Then decide whether the calculation is being used to release work, resequence work, size resources, protect a temporary condition, or explain a deviation.
The safest sequence is:
- Use readiness, constraint removal, schedule float, and handover formulas to decide whether work can be started or accepted.
- Use production-rate, Little’s Law, bottleneck, crane, truck, and closure-rate formulas to test whether the planned field flow is credible.
- Use temporary-works, hydrostatic pressure, maturity, reliability, and uncertainty formulas only as first-pass screens before specialist design, inspection, or testing.
- Tie every result to an action: proceed, hold, add capacity, resequence, inspect, repair, pump, brace, protect, or escalate for engineering review.
- Record the source of each input so the calculation can be audited after weather, access, design, procurement, or inspection conditions change.
Do not average away field constraints. A crew can be delayed by one missing permit, one blocked access route, one unapproved lift plan, one failed inspection, or one temporary-works hold even when the overall readiness percentage appears acceptable.
Basis and Validity Limits
Most formulas below assume that the activity boundary is clear, the schedule logic is current, the quantities match the latest drawings, and the resource rates come from comparable field conditions. They are reliable only when the calculation reflects the actual workface, sequence, access, inspection plan, weather exposure, material delivery pattern, and temporary condition.
The formulas are weak when the work scope is still changing, productivity is borrowed from a different construction method, the critical path logic is outdated, crew interference is ignored, material storage is constrained, inspection release is uncertain, or temporary works are treated as generic capacity instead of engineered systems.
Temporary load, water, maturity, reliability, and uncertainty checks are screening calculations. They do not replace a stamped design, method statement, lift plan, temporary-works coordinator review, geotechnical model, calibrated maturity curve, commissioning procedure, or permit condition. When failure could harm workers, the public, the asset, or the environment, the formula result should trigger the formal engineering control process.
Use conservative inputs when the consequence of being wrong is high. If the decision depends on uncertain productivity, pump capacity, curing temperature, equipment availability, water level, or inspection duration, show the pessimistic case and state whether the plan still works.
Work-Package Readiness
Readiness ratio:
Readiness percentage:
Weighted readiness when constraints do not have equal importance:
where x_i=1 when a constraint is cleared and x_i=0 when it is not.
A readiness score is not a release decision by itself. Missing excavation support, inspection hold point, access, lifting approval, groundwater control, or temporary works can block release even if the percentage looks high.
Critical Path Method
Early finish:
where ES is early start and D is duration.
Late start:
Total float:
Free float:
Project duration for a path:
The critical path is the path with the longest duration under the current logic. A near-critical path should be monitored because weather, procurement, inspection failure, or redesign can consume float quickly.
Worked Float Example
An activity has:
Then:
Total float:
The activity is not critical under the current logic, but a delay greater than five days affects the project completion date unless logic changes.
Percent Plan Complete and Constraint Removal
Percent plan complete:
Constraint removal ratio:
PPC measures reliability of commitments already made. CRR measures whether upcoming work is being made ready. Both are needed: a high PPC with weak constraint removal warns that future reliability may decline.
Production Rate and Crew Duration
Production quantity:
where r is production rate per crew or resource, N is number of crews or resources, and t is working time.
Required duration:
If effective work time per shift is reduced by setup, access, waiting, or inspection:
where U is productive utilization.
Adding labor helps only when the workface, supervision, materials, access, equipment, and inspections can support the added crews.
Little’s Law for Site Flow
Little’s Law:
where:
- L is average work, material, or units in the system;
- \lambda is throughput rate;
- W is average time in the system.
For site logistics, this can represent pallets in storage, trucks in cycle, workfaces awaiting inspection, or defects awaiting closeout.
If installed throughput is lower than delivery throughput, site inventory grows. That usually means more double handling, blocked access, damage, searching, and safety exposure.
Bottleneck Capacity
System capacity in a serial process:
Utilization of a resource:
For stable flow:
The construction bottleneck may be a gate, crane, hoist, crew, inspection hold point, concrete pump, access road, curing time, or information release. Improving a non-bottleneck resource does not increase total throughput.
Crane and Truck Cycle Time
Cycle time:
Unit throughput:
Required fleet size for a target delivery rate \lambda_{target}:
Use consistent units. If T_c is in hours, throughput is units per hour.
Cycle-time estimates should include waiting, hook time, signaling, exclusion zones, inspection checks, road restrictions, and cleanup. Ideal cycle time is rarely the field cycle time.
Temporary Works and Factored Loads
Factored design load:
where F_k is characteristic or nominal load and \gamma_F is the applicable load factor.
Load combination screening:
Utilization:
Temporary works pass the simple strength screen when:
This does not replace temporary-works design. Stability, deflection, bearing, settlement, uplift, impact, wind, construction sequence, inspection, and removal conditions must be checked.
Hydrostatic Pressure and Dewatering Screens
Hydrostatic pressure:
where \gamma_w is unit weight of water and h is water head.
Resultant force on a vertical rectangular surface with height h and width b:
Darcy seepage flow:
where k is permeability, i is hydraulic gradient, and A is flow area.
These are first-pass checks for excavations, retaining works, temporary drainage, cofferdams, and flooded work areas. Real dewatering design must check soil stratigraphy, drawdown, settlement, discharge permits, filters, clogging, pump redundancy, and monitoring.
Concrete Maturity Screen
Nurse-Saul maturity:
where:
- T_a is average concrete temperature during the interval;
- T_0 is datum temperature;
- \Delta t is time interval.
Strength relation from project-specific calibration:
Maturity is useful only after calibration to the mix, cementitious materials, curing condition, sensor placement, and acceptance method. It should not be used as a generic substitute for strength evidence.
Earned Value Field Metrics
Cost performance index:
Schedule performance index:
Cost variance:
Schedule variance:
Estimate at completion using current cost performance:
where EV is earned value, AC is actual cost, PV is planned value, and BAC is budget at completion.
Earned value should be tied to physically verified progress. Claiming earned value for work that lacks inspection release, test evidence, or rework closure can hide construction risk.
Reliability and Standby Equipment
Availability from MTBF and repair time:
Expected failures over operating time T:
For a critical pump, hoist, crane, generator, or dewatering system, availability must be interpreted through consequence. A short outage can still be unacceptable if it floods an excavation, interrupts a lift, or invalidates a concrete pour.
Risk Priority Number
where:
- S is severity;
- O is occurrence;
- D is detection rating.
Risk reduction:
RPN is a screening tool. High-consequence construction hazards such as excavation collapse, lifting failure, structural instability, or public interface failure require direct engineering review even if the RPN scale looks moderate.
Handover and Punch-List Closure
Closure rate:
Remaining duration at current closure rate:
First-pass completion ratio:
Handover is not complete because an asset is physically present. It requires accepted inspections, test certificates, commissioning records, as-built documents, operating procedures, training, defects status, and maintainable access.
Validation and Uncertainty
Combined uncertainty:
Conservative upper value:
Conservative lower value:
Use this for survey tolerances, concrete strength evidence, monitoring thresholds, settlement readings, deflection checks, water levels, and production measurements when uncertainty affects release.
Common Formula Mistakes
The most common mistake is using schedule duration as if it were physical production capacity. A bar on a schedule may hide access restrictions, curing time, material handling, inspection waits, utility conflicts, weather windows, and workface congestion. Duration formulas should be checked against the actual production system.
Another mistake is treating float as free time. Float can be consumed by procurement, redesign, failed inspections, safety holds, public interface constraints, and recovery work. If the float belongs to a path shared with other stakeholders, using it for one activity may transfer risk to another package.
Resource calculations are often optimistic because they ignore the bottleneck. Adding crews, trucks, or pallets does not improve throughput when the crane, hoist, gate, pump, inspection point, access road, or information release is already saturated. The calculation should name the controlling resource before recommending more capacity.
Temporary works and water calculations are sometimes treated as rough arithmetic rather than controlled engineering decisions. Excavation support, shoring, formwork, dewatering, traffic staging, lifting platforms, and temporary access must include sequence, inspection, monitoring, removal condition, and degraded state. A simple utilization ratio is not enough evidence for release.
Handover calculations can also be misleading when they count closed items without checking acceptance. A punch-list item, commissioning certificate, test result, as-built drawing, training record, or maintenance access issue is closed only when the responsible acceptance authority agrees that it is closed.
Validation Evidence Package
When using these formulas, ask:
- Does the formula represent the actual field boundary and sequence?
- Is the controlling constraint schedule logic, resource capacity, temporary works, inspection, water, access, or material supply?
- Is the result tied to a release, hold, resequence, repair, or handover decision?
- Does the calculation include degraded states, weather, equipment failure, or uncertainty where relevant?
- Which record proves the result: inspection, survey, test, counter, photo, model status, permit, or commissioning certificate?
- Who owns the next decision: superintendent, planner, engineer, temporary-works coordinator, quality inspector, safety lead, environmental lead, commissioning lead, or client representative?
- What change would invalidate the calculation: drawing revision, weather shift, access closure, supplier delay, failed test, changed sequence, equipment outage, or new permit condition?
Construction formulas are useful when they prevent a crew from starting work that is not ready, not safe, not inspectable, or not aligned with the engineering basis.