The bar bending schedule is signed. The estimator's sheet says 4,850 kg of 16 mm for the second-floor beams, the purchase order goes out at that plus the usual five percent — 5,092.5 kg — and six weeks later the yard invoice reads 5,300 kg, just over nine percent above the schedule. The allowance had already bought 242.5 kg of that gap on purpose. Nobody can say where the other 207.5 kg went, the roughly 4.1 percent above the purchase order that the allowance did not cover.
It went into offcuts. A bar bending schedule lists net cut lengths; a supplier sells stock bars in fixed commercial lengths. Every cut that does not divide neatly into a stock length leaves a remainder, and a remainder shorter than the shortest cut you still need is scrap. A flat percentage does not model that.
A wastage percentage feels like a property of the material. It is not. It is a property of the fit between your cut list and the stock length you buy: change the stock length and the number changes, change one cut by 200 mm and it can change. Two beam lines of identical tonnage can waste three percent and eighteen percent purely because of how their cuts pack. The naive arithmetic hides this, because dividing total length by stock length quietly assumes offcuts can be welded end to end and re-cut.
The working formula almost every Philippine estimator uses is kg/m = d² ÷ 162.2, with d the nominal diameter in millimetres. It is not a code provision, just a rounded constant from geometry and density.
Take steel at 7,850 kg/m³. A round bar's area is pi × d² ÷ 4 in mm², so pi × d² ÷ 4 ÷ 1,000,000 in m², and mass per metre is 7,850 × pi ÷ 4 ÷ 1,000,000 × d². Now 7,850 × 0.7853982 = 6,165.38, and 6,165.38 ÷ 1,000,000 = 0.00616538. Inverting, 1 ÷ 0.00616538 = 162.20. Checking the common sizes:
Rounded to three places, those read low for 16, 20 and 25 mm. The worked example below carries 16 mm as 1.5783 kg/m rather than 1.578, because a unit mass rounded down understates every single line, and this article is about under-ordering. The difference is under 0.03 percent and moves no conclusion, but it should not compound silently.
Two caveats. Under the bar standard named on your mill certificate, the nominal diameter of a deformed bar is that of a plain round bar of the same mass per metre, so the deformations are already inside the definition. That same standard allows a tolerance on mass per unit length, so a weighbridge ticket is not expected to match the nominal exactly — and that tolerance is precisely what decides whether the yard bills you on theoretical mass, meaning length times the nominal unit mass, or on actual weighed mass. Every peso figure in this article assumes theoretical.
Common market practice here is 6.0 m as the default stock length on the rack, with 7.5, 9.0, 10.5 and 12.0 m on order, mostly in the larger diameters and usually with a minimum quantity or a lead time. That is a market observation, not a standard requirement, so confirm it with your own supplier.
You are solving a bin-packing problem: fit a set of required pieces into the fewest fixed-size containers. The exact optimum for a real schedule is hard to compute. The site heuristic is first-fit-decreasing: sort every cut in that diameter longest to shortest, put each into the first already-opened stock bar that still has room, and open a new bar only when none has room. It is a heuristic, not an optimiser, with a published limit — the classical bin-packing result is that it never needs more than about eleven-ninths of the optimal bar count plus a small constant. In the example below it lands two bars above the best plan available, so treat its output as a starting plan a good bar bender will improve by eye.
An offcut is usable if it is at least as long as the shortest cut you still have to make in that diameter, after allowing for saw kerf and squaring the end; anything shorter is scrap by definition. Many yards also keep a blanket threshold near one metre, since most jobs have stirrups or dowels to absorb short pieces. That is common site practice, not a rule, and it only holds if someone tags and racks them.
The inputs, stated in full so every number below can be traced:
None of these are neutral, and each is something a reader would otherwise assume had been handled.
12 × 7.20 = 86.40 m. 8 × 5.40 = 43.20 m. 16 × 3.10 = 49.60 m. 24 × 1.85 = 44.40 m. Total net length = 86.40 + 43.20 + 49.60 + 44.40 = 223.60 m. Net mass = 223.60 × 1.5783 = 352.91 kg, or ₱20,468.78 of steel actually cast into the beam.
223.60 ÷ 12.0 = 18.63 stock bars, rounded up to 19. Then 19 × 12.0 = 228.00 m, and 228.00 × 1.5783 = 359.85 kg, or ₱20,871.30. Implied wastage = (228.00 - 223.60) ÷ 223.60 = 4.40 ÷ 223.60 = 1.97 percent. That figure is a fiction: it treats the 4.40 m of leftover as one continuous piece.
Sorted longest first, first-fit-decreasing gives this against 12.0 m stock:
Piece check: 7.20 m, 12 pieces. 5.40 m, 8. 3.10 m, 12 + 3 + 1 = 16. 1.85 m, 1 + 4 + 18 + 1 = 24. Cut length placed = 123.60 + 43.20 + 11.15 + 10.50 + 33.30 + 1.85 = 223.60 m, matching Step 1.
The plan needs 22 stock bars, not 19. Since the shortest required cut is 1.85 m, every offcut except bar 22's is scrap for this line; bar 22 leaves 10.15 m, a full usable length that goes back on the rack.
22 × 12.0 = 264.00 m purchased, so 264.00 × 1.5783 = 416.67 kg, or ₱24,166.86. Offcut length = 264.00 - 223.60 = 40.40 m. Cross-check: 12 × 1.70 = 20.40, plus 4 × 1.20 = 4.80, plus 0.85, plus 1.50, plus 3 × 0.90 = 2.70, plus 10.15, which sums to 40.40 m.
Purchased over net = 40.40 ÷ 223.60 = 18.07 percent, against the naive 1.97 percent. Be careful what you call that: it is a purchased-over-net ratio, not a waste rate. Of it, 30.25 m is genuine scrap on the article's own definition, 13.53 percent of net length, and bar 22's 10.15 m is the remaining 4.54 percent, a rackable offcut rather than a loss. Mass difference = 416.67 - 359.85 = 56.82 kg, which at ₱58.00 per kg is ₱3,295.56 missing from the estimate, on one beam line, in one diameter.
A bar bender will spot that 7.20 + 1.85 + 1.85 = 10.90 m and that 5.40 + 3.10 + 3.10 = 11.60 m. Twelve bars of the first pattern absorb all 12 long pieces and all 24 short ones; eight of the second absorb all 8 of the 5.40 m and all 16 of the 3.10 m pieces. That is 20 bars, 240.00 m, 378.79 kg, and wastage of 16.40 ÷ 223.60 = 7.33 percent. The refined plan saves 416.67 - 378.79 = 37.88 kg, or ₱2,197.04 — and is still 18.94 kg above the naive figure.
Here the arithmetic bites twice, because a 7.20 m cut cannot come out of a 6.0 m bar at all. Take a placeholder lap of 0.80 m for 16 mm, standing in for the designer's calculated splice length: each 7.20 m bar becomes two 4.00 m pieces, since 4.00 + 4.00 = 8.00 = 7.20 + 0.80. Treat that 0.80 m as low rather than typical — a Class B tension splice for a 16 mm Grade 415 bar in 21 MPa concrete commonly lands nearer 0.90 m, so the figures below understate the steel. The lap must come from the designer's calculation, and the splice has to sit where the design permits it, not where the cutting plan would like it. Lap splices also normally have to be staggered, so the pieces will not all be 4.00 m — half the bars at 4.00 and 4.00 and half at, say, 3.00 and 5.00 — which changes the cut list and the bar count.
Revised list: 24 pieces at 4.00 m, 8 at 5.40 m, 16 at 3.10 m, 24 at 1.85 m. Net length = 96.00 + 43.20 + 49.60 + 44.40 = 233.20 m, the original 223.60 m plus 12 × 0.80 = 9.60 m of lap. Net mass = 233.20 × 1.5783 = 368.06 kg. First-fit-decreasing then gives:
Total = 8 + 24 + 16 = 48 stock bars = 288.00 m. Offcut check: 8 × 0.60 = 4.80, plus 24 × 0.15 = 3.60, plus 16 × 2.90 = 46.40, giving 54.80 m, and 288.00 - 233.20 = 54.80 m. Mass = 288.00 × 1.5783 = 454.55 kg, or ₱26,363.90. Wastage is 54.80 ÷ 233.20 = 23.50 percent against the spliced net length. Measured against what the schedule originally asked for, purchased length is 64.40 ÷ 223.60 = 28.80 percent above the unspliced schedule, of which 4.29 percent is lap you cast and 24.51 percent is waste. Only the 54.80 m, the 23.50 percent, is wastage.
Both plans above are priced at the same ₱58.00 per kilogram, so the comparison is 454.55 kg against the refined plan's 378.79 kg: the 12.0 m bar is 75.76 kg, or ₱4,394.08, cheaper on this line. A longer bar often carries a length premium, so test that as a sensitivity rather than swapping the basis. At four percent, ₱58.00 × 1.04 = ₱60.32 per kg, the 20-bar plan costs 378.79 × 60.32 = ₱22,848.61 against ₱26,363.90 for the cheaper-per-kilogram 6.0 m bars, so the dearer bar is still ₱3,515.29 cheaper on the job. Break-even is ₱26,363.90 ÷ 378.79 = ₱69.60 per kg, a twenty percent premium: the long bar has to cost a fifth more per kilogram before the short one wins.
A flat allowance is an office convention, not a code requirement, and it is usable in the right conditions. Five percent here gives 352.91 × 1.05 = 370.56 kg: short of the refined 20-bar plan by 8.23 kg, or ₱477.34, which you can live with, and short of the first-fit plan by 46.11 kg, or ₱2,674.38, which you cannot.
It holds when cuts are short relative to stock, when marks repeat enough that offcuts get consumed, and when the offcut rack is genuinely used. It fails when cuts are long and awkward against the stock length, when marks are one-offs, and above all when a cut exceeds the stock length and forces splices you never priced.
A lap adds steel that stays permanently in the member, so it belongs in the net cut length before the cutting plan runs, never inside a wastage percentage. Waste is steel you buy and do not cast; lap is steel you buy and do cast. Mixing them makes both untraceable, and hides the fact that a shorter stock length can force laps a longer one would not.
Look again at the 6.0 m plan: 16 offcuts at 2.90 m, totalling 46.40 m, well above the 1.85 m threshold and genuinely usable. If other 16 mm marks need cuts of 2.90 m or less, and those pieces are tagged and racked instead of scrapped, effective consumption drops to 288.00 - 46.40 = 241.60 m, or 381.32 kg — within 2.53 kg of the best 12.0 m plan. In pesos, at the one basis used here, that is ₱22,116.56 against ₱21,969.82, so the short bar is now only ₱146.74 dearer instead of ₱4,394.08; under the four percent premium tested in Step 5 it flips outright, ₱22,116.56 against ₱22,848.61, and the short bar comes out ₱732.05 ahead. That swing needs bar-mark discipline: every offcut measured, tagged with diameter and length, racked by length, and checked against the next mark before a fresh bar is cut. Without it those 46.40 m are scrap. On a job with repeating floors this is one of the few estimating levers that pays back immediately.
Across a whole structure the bookkeeping is the hard part, not the arithmetic. The rebar module in the RHCES Estimator keeps cut lists separated by diameter and bar mark, which is the form you need before any cutting plan is worth running.
Many yards will, usually for a cutting charge and often against a minimum tonnage, and it is frequently the right call. Just understand what you are buying: the waste has not vanished, it has moved into their price or stayed on your site as their offcuts. Get a quotation both ways on the same cut list and compare delivered totals, not rates per kilogram.
Not all of it. Run a real cutting plan for the two or three diameters carrying most of the tonnage and most of the long cuts, and use a defensible flat allowance for the rest — waste on stirrups and ties is usually low, because short repetitive cuts pack efficiently. That is about an hour of work, and it is the difference between a wastage figure you can defend in a variation meeting and one you cannot.