Water Resources HubFree quick checks
Quick Engineering Checks
Plug-in calculators for working engineers: enter a few numbers, get an instant answer with the formula shown. No lessons, no sign-up — just the check you need, fast. For the full theory behind any check, follow the topic link under it.
Studying for the FE or PE Civil exam?
These checks verify your arithmetic — the exams test your judgement. Practise with free topic mini-quizzes with worked solutions, then a full timed practice exam.
40 checks across 8 task groups.
Concrete & steel
Rebar weight per metre
w = π/4 × d² × 7850
Weight of one reinforcing bar per metre run — for bar schedules and tonnage estimates.
Steel plate / section weight
W = t × b × L × 7850
Weight of a flat plate or built-up section from its dimensions — quick tonnage checks.
Concrete volume
V = L × W × D
Order quantity for slabs, footings, and walls — add 5–10% waste on top of the neat volume.
Concrete mix quantities (per m³)
dry vol = 1.52 × wet vol; cement = dry/(1+a+b) × 1440 kg/m³
Cement, sand, aggregate, and water per cubic metre for a nominal volumetric mix — planning estimates only.
Bolt shear capacity
R = n × 0.6 fu Ab
Nominal single- or double-shear capacity of one bolt — apply your code resistance factors to the result.
Fillet weld strength
R = 0.6 FEXX × 0.707 s × L
Nominal strength of a fillet weld group — apply your code resistance factors to the result.
Earthworks
Cut / fill volume (average end area)
V = (A1 + A2)/2 × L
Volume between two cross-sections — the workhorse earthwork quantity.
Earthwork haul cost
Cost = V × rate
Budget estimate for moving excavated material — rate should include loading, haul, and dump.
Hydraulics
Hydrostatic force
F = γ hc A
Resultant force on gates, dams, and tank walls — use the centroid depth, not the top edge.
Reynolds number
Re = V D / ν
Flow regime check: below ~2,300 laminar, above ~4,000 turbulent in pipes.
Darcy–Weisbach head loss
hf = f (L/D) V²/(2g)
Friction loss in a pipe run — get f from Moody/Colebrook first.
Hazen–Williams pipe flow
V = 0.85 C R0.63 S0.54 Q = VA
Velocity and discharge in a full circular water pipe — water only, 20 °C.
Manning's full-pipe discharge
Q = (1/n) A R2/3 S1/2
Full-flow capacity of a circular pipe or sewer — the gravity-design starting point.
Rational method runoff
Q = C i A / 360 (i in mm/h, A in ha)
Peak runoff from small urban catchments — keep the catchment under ~80 ha.
Pump power
P = γ Q H / η
Shaft power at the operating point — size the motor with margin above this.
Water hammer surge (Joukowsky)
Δp = ρ a ΔV ΔH = aΔV/g
Pressure rise from a sudden velocity change — rapid valve closure or pump trip.
USLE soil loss
A = R × K × LS × C × P
Average annual sheet-and-rill erosion — multiply by area for gross watershed loss.
Orifice flow
Q = Cd A √(2gh)
Discharge through a submerged orifice — tank outlets, underflow gates, detention orifices.
Rectangular weir flow
Q = 1.84 L H1.5 (SI)
Flow over a suppressed rectangular weir — spillways, channel controls, measurement flumes.
Thrust block force
F = 2 p A sin(θ/2)
Unbalanced thrust at a bend or tee — size the concrete block or restrained joint for this.
Pipe velocity check
V = Q / A
Velocity check against the usual 0.6–3.0 m/s water-pipe limits.
Clarifier surface overflow rate
SOR = Q / A
Surface loading on a circular clarifier — typical design 20–40 m/d for primary.
Structures
Simply supported beam — point load
RA = Pb/L RB = Pa/L Mmax = RAa
Reactions and peak moment for a point load — the first check on any beam sketch.
Simply supported beam — UDL
R = wL/2 Mmax = wL²/8
Reactions and midspan moment under uniform load.
Cantilever deflection (tip load)
δ = PL³/(3EI)
Tip deflection of a cantilever — quick serviceability check.
Bending stress (rectangular section)
σ = My/I I = bh³/12
Extreme-fibre stress in a rectangular beam — compare with the allowable stress.
Euler buckling load
Pcr = π²EI/(KL)²
Critical elastic buckling load of a column — check slenderness limits apply first.
Rebar development length (ACI, simplified)
ld = fy/(2.1√f′c) × db (SI)
Tension development length for uncoated bars, normal-weight concrete — simplified; check code modifiers.
One-way slab minimum thickness (ACI)
h = l/20 (simple) · l/24 (one cont.) · l/28 (both) · l/10 (cantilever)
Minimum thickness to skip deflection calculations — ACI 318 table values.
Geotech
Terzaghi bearing capacity (strip)
qult = cNc + γDfNq + 0.5γBNγ
Ultimate bearing capacity of a strip footing — divide by your factor of safety for allowable.
Rankine active earth pressure
Ka = tan²(45° − φ/2) pa = KaγH
Active pressure distribution behind a retaining wall — resultant acts at H/3.
Retaining wall stability (FS)
FSot = ΣMR/ΣMO FSsl = μΣW/Pa
Overturning and sliding factors of safety — usually target ≥ 1.5 and ≥ 1.5.
Transport
Stopping sight distance
SSD = 0.278Vt + V²/(254(f ± G)) (V in km/h)
Minimum sight distance for a design speed — the +/− grade term adjusts braking distance.
Horizontal curve radius
R = V²/(127(e + f)) (V in km/h)
Minimum radius for a design speed, superelevation, and side friction.
Vertical curve high/low point
x = g1L/(g1 − g2) (from PVC)
Station of the crest/sag high or low point — for drainage and sight checks.
Environmental
BOD loading
Load = Q(MLD) × BOD(mg/L) (kg/d)
Daily organic load to a treatment plant — the first number in any plant check.
Dilution / mixing
C2 = C1V1/(V1 + V2)
Concentration after mixing a dosed volume into a larger one — chemical dosing, spill dilution.
Math & general
Normal distribution probability
P(Z ≤ z) = Φ(z)
Cumulative standard-normal probability — hypothesis tests, confidence intervals, reliability.
Compound amount (F/P)
F = P(1 + i)n
Future worth of a present sum — the first engineering-economics factor.
Unit converter
value × (from-factor / to-factor)
Length, pressure, flow, volume, and area conversions between SI and US units.
For study and checking only. These quick checks run entirely in your browser — nothing is sent anywhere. They use standard textbook formulas with everyday assumptions (water at 20 °C, γ = 9.81 kN/m³, steel at 7850 kg/m³); always apply your jurisdiction's codes, load factors, and resistance factors before using a number in design.