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The hooked bar, which sets both the development length and the bend geometry.
Bar diameter enters the development length raised to the power of one and a half, so it dominates the answer: a #8 hook is not twice a #4 hook, it is nearly three times it. Bar size also decides the minimum bend diameter, which steps up at #9.
Whether the bar turns a quarter turn or doubles fully back on itself.
The angle does not change the development length — both standard hooks develop the same ldh — but it changes the geometry entirely. A 180 degree hook is far more compact in the direction of the bar, and on every size above #3 it needs LESS steel to make, because the 4db tail saves more than the extra half turn of arc costs. Run both and compare the allowance line.
The specified compressive strength of the concrete the hook is embedded in.
It acts twice: once through the square root in the denominator, and again through the concrete-strength factor, which penalises mixes below 6,000 psi (41 MPa) on a sliding scale rather than a step. Above that the factor sits at unity and only the square root keeps working.
The specified yield strength of the hooked bar.
The development length is directly proportional to it, because ldh exists to deliver the bar's full yield force into the concrete. Grade 80 and Grade 100 reinforcement therefore need proportionally deeper hooks than the Grade 60 most US detailing assumes.
Whether the bar carries an epoxy coating.
Coating reduces the bond between steel and concrete, and the hook provision answers with a flat 1.2 multiplier — lighter than the tension straight-bar penalty, because a hook develops much of its capacity through bearing inside the bend rather than through bond along its length.
Whether ties or stirrups enclose the hook to the code's own requirement.
A hook fails by splitting the concrete outward from the inside of the bend, and steel wrapped around that zone resists the split directly. The difference is 1.0 against 1.6 — the largest single factor in this calculation, and the cheapest one to earn.
Whether the tail sits inside a confined core or in ordinary cover.
Side cover behind the tail is what stops the hook prising a face off the member. Generous cover, or the surrounding steel of a column core, earns unity; everything else carries a 1.25 penalty. Measure the cover to the side of the bar, not to the plane of the hook.
Enter 1.0 for normal-weight concrete and 0.75 for all-lightweight.
Lightweight aggregate splits more readily than normal-weight, so the same hook develops less. Sand-lightweight mixes fall between the two limits and the code gives an interpolation; take the value from your mix rather than assuming the worse case.
Hooked-bar development length ldh
14.8 in
ldh is measured from the critical section to the far outside of the bend, not to the start of the bend and not to the end of the tail. Detailing it to the wrong reference point is the commonest way a hook ends up short in the field.
- Minimum inside bend diameter
- 3.75 in
- Tail extension beyond the bend
- 7.5 in
- Bar consumed by the bend and tail
- 10.94 in
- Code floor for this bar
- 6 in
- Length the equation alone gives
- 14.77 in
- Concrete strength factor applied
- 0.87 x ldh
- Confinement and location factors combined
- 2 x ldh
They open the calculator with your figures already in it
Rebar Standard Hook Development and Cut-Length Calculator: 14.77 in — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- ACI 318-19 development of standard hooks in tension: ldh = [fy x psi_e x psi_r x psi_o x psi_c / (55 x lambda x sqrt(f'c))] x db^1.5, worked in pounds and inches, and never less than the greater of 8db and 6 in. ldh is measured from the critical section to the far OUTSIDE of the bend
- Modification factors from the same provision: psi_e is 1.2 for epoxy-coated bar and 1.0 otherwise; psi_r is 1.0 where the hook is enclosed by confining reinforcement as the code requires and 1.6 where it is not; psi_o is 1.0 for a hook terminating inside a column core with at least 2.5 in of side cover or with side cover of at least 6db, and 1.25 otherwise; psi_c is f'c/15,000 + 0.6 below 6,000 psi and 1.0 at or above it
- ACI 318 Table 25.3.1 standard hook geometry: minimum inside bend diameter 6db for #3 through #8 and 8db for #9 through #11; tail extension 12db for a 90 degree hook, and the greater of 4db and 2.5 in for a 180 degree hook
- ACI 315 Guide to Presenting Reinforcing Steel Design Details — the detailing convention the cut-length allowance follows. The allowance itself is the developed centreline length of the bend arc plus the tail, which is geometry rather than a published table
Inputs used
- Bar Size
- #5 (5/8 in, 15.9 mm)
- Hook Angle
- 90 degrees — tail extension of 12db
- Concrete Strength f'c
- 4000 psi
- Steel Yield Strength fy
- 60000 psi
- Epoxy Coating
- Uncoated or zinc-coated bar
- Confining Reinforcement at the Hook
- No qualifying confining reinforcement
- Where the Hook Terminates
- Any other location
- Lightweight Concrete Factor (lambda)
- 1
Intermediate steps
- Minimum inside bend diameter
- 3.75 in
- Tail extension beyond the bend
- 7.5 in
- Bar consumed by the bend and tail
- 10.94 in
- Code floor for this bar
- 6 in
- Length the equation alone gives
- 14.77 in
- Concrete strength factor applied
- 0.87 x ldh
- Confinement and location factors combined
- 2 x ldh
Confidence note: ldh is measured from the critical section to the far outside of the bend, not to the start of the bend and not to the end of the tail. Detailing it to the wrong reference point is the commonest way a hook ends up short in the field.
What this calculation does not cover
- Written for #11 bars and smaller; #14 and #18 hooks carry different factor conditions and are not offered.
- Tension hooks only. Hooks developed in compression are governed by separate provisions.
- The cut-length allowance is centreline geometry; a shop's own bend deduction table may differ slightly and should win.
- Confirm the equation form against the edition of ACI 318 your jurisdiction has adopted — earlier editions used a different expression.
Add the equipment this sizes
This result is a specification — 14.8 in — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-01 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations4
- ACI 318-19 development of standard hooks in tension: ldh = [fy x psi_e x psi_r x psi_o x psi_c / (55 x lambda x sqrt(f'c))] x db^1.5, worked in pounds and inches, and never less than the greater of 8db and 6 in. ldh is measured from the critical section to the far OUTSIDE of the bend
- Modification factors from the same provision: psi_e is 1.2 for epoxy-coated bar and 1.0 otherwise; psi_r is 1.0 where the hook is enclosed by confining reinforcement as the code requires and 1.6 where it is not; psi_o is 1.0 for a hook terminating inside a column core with at least 2.5 in of side cover or with side cover of at least 6db, and 1.25 otherwise; psi_c is f'c/15,000 + 0.6 below 6,000 psi and 1.0 at or above it
- ACI 318 Table 25.3.1 standard hook geometry: minimum inside bend diameter 6db for #3 through #8 and 8db for #9 through #11; tail extension 12db for a 90 degree hook, and the greater of 4db and 2.5 in for a 180 degree hook
- ACI 315 Guide to Presenting Reinforcing Steel Design Details — the detailing convention the cut-length allowance follows. The allowance itself is the developed centreline length of the bend arc plus the tail, which is geometry rather than a published table
Which documents these citations point at
Standards referenced: ACI 318-19, ACI 318, ACI 315 (American Concrete Institute, United States).
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Tools and safety for this job
To fix reinforcement. Generic types, no brands, no prices.
Protection this work requires
- Saws, grinders and breakers run above 85 dB, where hearing damage accumulates and does not recover: defenders or plugs for every cut, not just the long ones.
- Breakers and grinders cause permanent nerve damage: limit continuous trigger time, keep hands warm, and stop if fingers tingle or blanch.
- Boards, blocks and bagged material cause most lasting back injuries on small sites: two people or a lifter for full sheets, and never a bag on one shoulder up a ladder.
- Nailing, chiselling and cutting all throw fragments: glasses to EN 166 or ANSI Z87.1, and goggles rather than glasses overhead.
Show the 4 tools this job needsHide tools
Essential
Tape measure
Recommended
Rebar cutter and bender
Rebar tying tool
Optional
Angle grinder
Also needed as materials: cutting and diamond discs, tie wire.
what each concrete tool is for, and the spec that decides which to buy where one does.
This 90 degree hook develops 14.8 in (375 mm) measured to the outside of the bend, and takes 10.9 in (278 mm) of bar to make once the 3.8 in (95 mm) bend diameter and the tail are accounted for. Add that allowance to the straight legs when the cut list is written, or the fabricator's bar will be short by the bend.