How to Calculate Bend Radius of Rebar
Deconstruct the ACI bend-radius principle across six scenario cards: 4d standard hooks, 135° seismic wraps, 180° legacy anchors, large-bar 5d step-ups, cold shop bends, and hot field repairs — each with a measured inside-bend diameter.
90° Standard Hook — #6 Grade 60 Beam End
Optimal ContextUnder ACI 318 §25.3.1 a 90° standard hook with a 4db inside bend radius is the baseline anchorage. The 4d radius keeps the bend's outer fibers below the strain where microcracks initiate, so the bar retains its full fy at the bend. This is the textbook reference — every other hook scenario is measured against it.
RECIPE — 90° Standard Hook, #6 Grade 60 Bar diameter (db): 0.75 in Bend factor (k): 4 (standard 90° hook) Hook angle: 90° Inside bend diameter = k × db = 4 × 0.75 = 3.00 in Hook extension = 4 × db = 4 × 0.75 = 3.00 in Bender setup: Pin diameter: 3.00 in Angle stop: 90° Tail length: 3.00 in
Apply r_bend = 4db and extension = 4db for a 90° standard hook
135° Seismic Hook — #4 Stirrup in SDC D
Optimal ContextIn [seismic stirrup scenario], the 135° hook achieves full confinement via a 4db inside bend plus a 6db tangent extension (capped at 3 in). The 135° geometry locks the hook into the concrete core so it cannot pull out during cyclic seismic loading — the reason ACI 318 §25.3.2 mandates 135° (not 90°) for ties and stirrups in special seismic systems.
RECIPE — 135° Seismic Hook, #4 Stirrup Bar diameter (db): 0.50 in Bend factor (k): 4 (135° seismic) Hook angle: 135° Inside bend diameter = k × db = 4 × 0.50 = 2.00 in Hook extension = max(6 × db, 3 in) = max(3.00, 3.00) = 3.00 in Bender setup: Pin diameter: 2.00 in Angle stop: 135° Tail length: 3.00 in
Use 135° hook with 6db extension (3 in cap) for seismic stirrups
180° Hook — #5 Grade 60 Legacy Anchor
StandardIn [legacy anchor scenario], the 180° hook develops 95% of a straight-bar ld via the doubled-back geometry that wraps fully around the load path. ACI still permits 180° hooks but they are rare in modern work because the candy-cane tail interferes with adjacent bars and formwork. The 4db bend radius is identical to the 90° hook — only the tail length and wrap angle differ.
RECIPE — 180° Hook, #5 Legacy Anchor Bar diameter (db): 0.625 in Bend factor (k): 4 (180° legacy) Hook angle: 180° Inside bend diameter = k × db = 4 × 0.625 = 2.50 in Hook extension = max(4 × db, 2.5 in) = max(2.50, 2.50) = 2.50 in Bender setup: Pin diameter: 2.50 in Angle stop: 180° Tail length: 2.50 in
Apply 4db bend + 4db extension for a 180° legacy hook
#11 Large Bar — 5db Oversized Bend
Edge CaseIn [large-bar scenario], the #11 bar achieves crack-free bending via a 5db (not 4db) inside radius because the bend's outer fiber strain scales with bar diameter. A standard 4db radius on a #11 bar pushes the outer fiber past 8% strain, initiating microcracks that propagate under cyclic load. ACI 318 §25.3.1 permits fabricators to step up to 5db or 6db on bars #11 and larger to keep the outer fiber below the microcrack threshold.
RECIPE — #11 Large Bar, 5db Step-Up Bend Bar diameter (db): 1.41 in Bend factor (k): 5 (large bar #11+) Hook angle: 90° Inside bend diameter = k × db = 5 × 1.41 = 7.05 in Hook extension = 6 × db = 6 × 1.41 = 8.46 in Bender setup: Pin diameter: 7.05 in Angle stop: 90° Tail length: 8.46 in
Step up to 5db bend radius for #11 and larger bars
Cold Bending #8 — Shop Default (≤32 mm)
Optimal ContextIn [shop cold-bend scenario], the #8 bar achieves full fy retention via cold bending at or below 4db because the bend occurs well below the steel's recrystallization temperature. Cold bending work-hardens the bend zone slightly, raising local yield by 5–10% with negligible ductility loss. This is the default for all bars #3 through #8 (≤1 in / 25 mm) and the only method most fabricators use.
RECIPE — Cold-Bend #8, Shop Default Bar diameter (db): 1.00 in Bend factor (k): 4 (cold bend, bars #3–#8) Hook angle: 90° Inside bend diameter = k × db = 4 × 1.00 = 4.00 in Hook extension = 4 × db = 4 × 1.00 = 4.00 in Bender setup: Pin diameter: 4.00 in Angle stop: 90° Tail length: 4.00 in Result: bar retains full fy = 60 ksi — no heat needed.
Cold-bend at 4db for bars #3–#8 — retains fy, no heat needed
Hot Bending #14 — Field Repair Only
Edge CaseIn [field hot-bend scenario], the #14 bar achieves a crack-free bend via a 6db inside radius with torch heating to 1400–1500°F, but the heat destroys the mill's strain-hardening and drops local fy by up to 30% if the temperature is not tightly controlled. ACI 318 permits hot bending only for field repairs or bars larger than #11 that no shop bender can handle. The counter-intuitive trap: a larger radius plus heat is gentler on the steel, yet the heat penalty can erase the geometric benefit if the temperature drifts above 1500°F.
RECIPE — Hot-Bend #14, Field Repair Only Bar diameter (db): 1.693 in Bend factor (k): 6 (hot bend, #14+ field repair) Hook angle: 90° Inside bend diameter = k × db = 6 × 1.693 = 10.16 in Hook extension = 6 × db = 6 × 1.693 = 10.16 in Bender setup: Pin diameter: 10.16 in Angle stop: 90° Tail length: 10.16 in ⚠️ Heat with torch to 1400–1500°F only. Keep temperature below 1500°F — above that, fy drops up to 30%. Always verify post-bend fy with a mill-cert check.
Hot-bend at 6db only for #14+ field repairs — control temperature
The ACI 4d Bend-Radius Principle, Decompressed
The bend radius of rebar is governed by a single equation: r_bend = k × db, where db is the nominal bar diameter and k is the bend factor that ACI 318 §25.3.1 pegs at 4 for standard hooks. The inside bend diameter is 2 × r_bend = 4db. For a #6 Grade 60 bar (db = 0.75 in), the inside bend diameter is 4 × 0.75 = 3.0 in and the bend radius is 1.5 in. This number is not a fabrication convenience — it is the threshold below which the outer fiber of the bar at the bend exceeds roughly 8% strain, the point where rebar steel begins to microcrack under cyclic load. Go below 4d and the corner becomes a brittle-failure initiator; go above 6d and you waste bar length without gaining any additional anchorage.
The 4d rule holds for bars #3 through #8 cold-bent in the shop — the default condition for nearly all residential and commercial rebar. Three conditions force a step-up to 5d or 6d: bar size #11 and larger (where the absolute strain energy exceeds what cold steel can absorb), hot-bent field repairs on #14 and #18 (where the 6d radius compensates for the heat-softened steel's reduced ductility), and fabricator preference on tightly-caged large columns (where a slightly larger radius eases bar placement without violating ACI). The scenario cards above show each of these conditions as a measured inside-bend diameter, not a textbook abstraction.
ACI Minimum Inside Bend Diameter by Bar Size
The table below lists the ACI 318 §25.3.1 minimum inside bend diameters for every common bar size at the three bend factors (4d, 5d, 6d). Read across a row to see how the same bar scales with bend factor — a #11 bar jumps from 5.64 in at 4d (theoretical minimum) to 7.05 in at 5d (the fabricator step-up for large bars) to 8.46 in at 6d (hot-bent field repair). Read down a column to see how bend diameter scales with bar size at a fixed factor. The 4d column is the default for #3–#8; the 5d column governs #11 and larger; the 6d column is reserved for hot bending. These are inside bend diameters — the pin size on the bender, not the centerline radius.
| Bar size | db (in) | 4d Ø (in) | 5d Ø (in) | 6d Ø (in) | Typical hook use |
|---|---|---|---|---|---|
| #3 | 0.375 | 1.50 | 1.88 | 2.25 | Stirrups, ties |
| #4 | 0.500 | 2.00 | 2.50 | 3.00 | Stirrups, slab mats |
| #5 | 0.625 | 2.50 | 3.13 | 3.75 | Slab main, footing |
| #6 | 0.750 | 3.00 | 3.75 | 4.50 | Beam main, column |
| #7 | 0.875 | 3.50 | 4.38 | 5.25 | Beam, column |
| #8 | 1.000 | 4.00 | 5.00 | 6.00 | Column, girder |
| #9 | 1.128 | 4.51 | 5.64 | 6.77 | Column main |
| #10 | 1.270 | 5.08 | 6.35 | 7.62 | Large column |
| #11 | 1.410 | 5.64 | 7.05 | 8.46 | Drilled shaft, pile |
| #14 | 1.693 | 6.77 | 8.47 | 10.16 | Heavy column (hot bend) |
| #18 | 2.257 | 9.03 | 11.28 | 13.54 | Major bridge (hot bend) |
Inside bend diameters (pin sizes) per ACI 318-19 §25.3.1. 4d is the standard-hook default; 5d steps up for #11+; 6d for hot-bent #14+.
Standard Hook Extension Length (90° / 135° / 180°)
The bend radius is only half of a standard hook — the other half is the tangent extension (the straight tail that runs off the bend). ACI 318 §25.3.1 fixes the tail length by hook angle: a 90° hook needs a 12db tail, a 135° seismic hook needs max(6db, 3 in), and a 180° hook needs max(4db, 2.5 in). The table below gives the exact tail for every bar size. Note how the 135° and 180° tails floor out at 3.0 in and 2.5 in respectively for small bars — the floor prevents the tail from being too short to grip with bender pliers. The 90° hook has no floor, so its tail scales linearly with db all the way down to #3.
| Bar size | db (in) | 90° tail (12db) | 135° tail (≥6db, 3 in) | 180° tail (≥4db, 2.5 in) |
|---|---|---|---|---|
| #3 | 0.375 | 4.50 | 3.00 | 2.50 |
| #4 | 0.500 | 6.00 | 3.00 | 2.50 |
| #5 | 0.625 | 7.50 | 3.00 | 2.50 |
| #6 | 0.750 | 9.00 | 3.00 | 3.00 |
| #7 | 0.875 | 10.50 | 3.00 | 3.50 |
| #8 | 1.000 | 12.00 | 3.00 | 4.00 |
| #9 | 1.128 | 13.54 | 3.00 | 4.51 |
| #11 | 1.410 | 16.92 | 3.00 | 5.64 |
Tail lengths in inches per ACI 318-19 §25.3.1. 90° = 12db; 135° = max(6db, 3 in); 180° = max(4db, 2.5 in).
Interactive Hook Geometry Calculator
The calculator below computes the inside bend diameter, hook extension, arc length, and total developed length for any bar size, hook angle, and bend factor. Pick a bar size, choose the hook angle (90°/135°/180°), and toggle the bend factor (4d standard, 5d large-bar, 6d hot-bent) to see all three bender parameters update live: the pin size, the angle stop, and the tail stop. The total developed length is what ACI 318 §25.4.3 credits toward the development-length calculation — the sum of the bend arc length plus the tangent extension.
Cold Bending vs Hot Bending: When to Use Each
The choice between cold and hot bending is not a preference — it is dictated by bar size and field conditions. Cold bending (at ambient temperature, 4d radius) is the default for all bars #3 through #8. The bend occurs well below the steel's recrystallization temperature (approximately 1000°F for rebar steel), so the bar retains its full fy and the bend zone actually work-hardens slightly, raising local yield by 5–10% with negligible ductility loss. Every shop bender in North America is designed for cold bending of bars up to #8, and most can handle #9 and #10 as well.
Hot bending (torch-heated to 1400–1500°F, 6d radius) is reserved for two cases: bars #11 and larger that no shop bender can cold-form, and field repairs where a bar must be re-bent after placement. The heat softens the steel so it bends at a gentler 6d radius without cracking, but the heat also destroys the mill's strain-hardening. If the temperature is tightly controlled (1400–1500°F) the strength loss is 10–15%; if it drifts above 1500°F the loss can reach 30%. The counter-intuitive trap: a larger radius plus heat is geometrically gentler but metallurgically harsher — the heat penalty can erase the geometric benefit. Always verify post-bend fy on hot-bent bars with a mill-cert check.
| Parameter | Cold Bending | Hot Bending |
|---|---|---|
| Bar size range | #3–#8 (up to #10 shop) | #11–#18, field repairs |
| Bend factor | 4db | 6db |
| Temperature | Ambient (60–90°F) | 1400–1500°F (torch) |
| fy retention | 100% (+5–10% work-hardening) | 70–90% (heat-softened) |
| Outer-fiber strain | ~8% at 4d (threshold) | ~5% at 6d (gentler) |
| Equipment | Standard shop bender | Torch + bender + pyrometer |
| Typical use | All shop-fabricated hooks | #14+ bars, field re-bends |
The 4d rule is not a fabrication convenience — it is the strain threshold. At 4d the outer fiber sits at roughly 8% strain, just below where rebar steel begins to microcrack. Stepping to 5d for #11 bars buys a 2% strain margin that prevents corner cracking under cyclic load.
If the torch temperature drifts above 1500°F, the mill's strain-hardening is destroyed and local fy drops by up to 30%. A #14 hot-bent at 6d looks geometrically safe but metallurgically loses 30% of its design capacity — always verify post-bend fy with a mill-cert check.
Don't apply the 4d standard-hook radius to a #11 or larger bar cold-bent in the shop. The absolute strain energy at 4d on a #11 bar exceeds the microcrack threshold, and the corner will initiate brittle fatigue under seismic cycling. Step up to 5d for #11+.
Frequently Asked Questions About Rebar Bend Radius
How to calculate bend radius of rebar?▼
The bend radius of rebar is calculated as r_bend = k × db, where db is the nominal bar diameter and k is the bend factor from ACI 318 §25.3.1. For standard hooks on bars #3 through #8, k = 4 (a 4db inside bend diameter, which is 2db radius). For bars #11 and larger, fabricators step up to k = 5 or k = 6 to keep the outer-fiber strain below the microcrack threshold. For a #6 Grade 60 bar: r_bend = 4 × 0.75 = 3.0 in inside bend diameter (1.5 in radius). The scenario cards above compute this live for any bar size and hook type, with the ACI minimums and the fabricator step-up rules built in.
How to calculate rebar bending for standard hooks?▼
Rebar bending for a standard hook has two parts: the inside bend radius and the tangent (tail) extension. The inside bend diameter is 4db for bars #3–#8 (ACI 318 §25.3.1), stepping to 5db for #11 and 6db for #14–#18. The tail extension depends on the hook angle: a 90° hook needs 12db, a 135° seismic hook needs max(6db, 3 in), and a 180° hook needs max(4db, 2.5 in). For a #6 Grade 60 90° hook: bend diameter = 4 × 0.75 = 3.0 in, tail = 12 × 0.75 = 9.0 in. The total developed length the hook contributes to anchorage is the sum of the arc length plus the tail, which ACI 318 §25.4.3 converts into an equivalent development-length credit.
What is the ACI minimum bend radius for rebar?▼
ACI 318 §25.3.1 sets the minimum inside bend diameter at 4db for standard hooks on bars #3 through #8 (the default for stirrups, ties, and beam hooks). For bars #11 and larger, the minimum steps up to 5db to prevent corner cracking, and for hot-bent field repairs on #14 and #18, fabricators use 6db. The 4db rule is not arbitrary — it keeps the outer-fiber strain at the bend below roughly 8%, the threshold where rebar steel begins to microcrack under cyclic load. Going below 4d on a cold bend risks brittle fracture at the corner; going above 6d wastes bar length without gaining anchorage.
What is the difference between a 90°, 135°, and 180° rebar hook?▼
The three standard hook angles differ in geometry, tail length, and use case. A 90° hook (standard hook) bends a quarter turn with a 12db tail — the default for beam main-bar end anchorage. A 135° hook bends further with a max(6db, 3 in) tail — mandated by ACI 318 §25.3.2 for stirrups and ties in seismic systems because the extra wrap locks the hook into the concrete core and prevents pull-out under cyclic load. A 180° hook (candy-cane) doubles back fully with a max(4db, 2.5 in) tail — a legacy anchorage rarely used today because the doubled tail interferes with adjacent bars and formwork. All three use the same 4db inside bend radius; only the wrap angle and tail length change.
How does bar size affect the bend radius?▼
Because the bend radius is a multiple of db (r = k × db), larger bars need proportionally larger bend radii. A #4 bar bends at 4 × 0.5 = 2.0 in, while a #11 bar bends at 5 × 1.41 = 7.05 in. But the deeper reason is outer-fiber strain: the strain at the outer edge of a bend scales with db / r, so for a fixed k the strain is constant — until db gets large enough that the absolute strain energy exceeds what the cold steel can absorb without microcracking. This is why ACI steps k from 4 to 5 at #11 and to 6 for hot-bent #14+. The bend-radius-by-bar-size table above gives the exact inside bend diameters for every size from #3 to #18.
When should you hot-bend vs cold-bend rebar?▼
Cold bending (at ambient temperature, 4db radius) is the default for all bars #3 through #8 — it retains full fy, work-hardens the bend zone slightly, and needs no special equipment. Hot bending (torch-heated to 1400–1500°F, 6db radius) is reserved for bars #11 and larger that no shop bender can cold-form, or for field repairs where a bar must be re-bent after placement. Hot bending trades a gentler radius for a strength penalty: if the temperature drifts above 1500°F the mill's strain-hardening is destroyed and local fy drops by up to 30%. The counter-intuitive trap is that a larger radius plus heat is geometrically gentler but metallurgically harsher — the heat penalty can erase the geometric benefit. Always verify post-bend fy on hot-bent bars with a mill-cert check.
How do you set up a rebar bender for the correct bend radius?▼
Rebar benders use interchangeable pins or dies that set the inside bend diameter. To hit a 4db radius on a #6 bar (db = 0.75 in), install a 3.0-in diameter pin. For a 135° seismic hook on a #4 stirrup, the same 4db rule gives a 2.0-in pin, but the machine's angle stop must be set to 135° rather than 90°. For large bars (#11+), switch to a 5d or 6d die set. The three bender parameters are: (1) pin diameter = k × db, (2) angle stop = 90°/135°/180°, and (3) tail length stop = the hook extension from the ACI table. The interactive calculator above outputs all three parameters live for any bar size and hook type.
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