Compute required tension development length ld per ACI 318-19 §25.5.2 with all five modification factors (ψt, ψe, ψs, ψg, λ), automatic (cb+Ktr)/db capping, and a pass/fail check against your provided length.
Inputs
Bar properties
psi
Concrete properties
psi
Confinement geometry
Enter the clear cover to the bar surface and clear spacing between bars. These determine cb and the epoxy modification factor branch.
in
in
Provided development length (pass/fail check)
in
Results
Fill inputs above to see results.
How it works
ACI 318-19 §25.5.2 gives the general development length equation for deformed bars in tension:
All quantities in consistent units (psi & inches, or MPa & mm).
The ratio (cb+Ktr)/db is capped at 2.5 per §25.5.2.1.
The minimum ld is 12 in (300 mm) per §25.5.2.1.
This calculator uses Ktr = 0 (conservative; no transverse reinforcement credit).
ψt — Bar location
Top bar (>12 in. fresh concrete below): 1.3
All other positions: 1.0
ψe — Coating
Epoxy, cover <3db or spacing <6db: 1.5
Other epoxy-coated: 1.2
Uncoated or zinc-coated: 1.0
ψt·ψe ≤ 1.7
ψs — Bar size
#3–#6 (10M–20M): 0.8
#7 and larger (25M+): 1.0
What is development length and why does it matter?
Development length (ld) is the minimum embedment length needed for a deformed reinforcing bar to develop its full yield strength through bond stress between steel and concrete. If a bar is cut short, the surrounding concrete cannot transfer enough force before the steel slips — causing brittle, sudden failure. ACI 318-19 §25.5 sets the minimum required ld so that the bar reaches fy at the critical section before bond failure occurs.
Why is the (cb+Ktr)/db ratio capped at 2.5?
The ratio represents the degree of confinement available to prevent splitting failure along the bar. ACI research showed that beyond a ratio of 2.5, the mode of failure shifts from splitting to bar pull-out — and the formula becomes non-conservative. Capping at 2.5 per §25.5.2.1 keeps the equation on the safe side regardless of how much cover or transverse reinforcement is provided. Ignoring the cap would produce unrealistically short development lengths.
What is Ktr and why does this calculator set it to zero?
Ktr = 40Atr/(sn) is a transverse reinforcement index that credits ties or stirrups for resisting splitting. Atr is the total area of transverse steel within spacing s crossing the potential splitting plane, and n is the number of bars being developed. Setting Ktr=0 is explicitly permitted by ACI 318-19 as a conservative simplification (§25.5.2.1 commentary). It is the most common design approach and eliminates the need to iterate on stirrup details during initial bar design. If you have heavy transverse reinforcement, the actual ld can be shorter — but a value of Ktr=0 is always safe.
When does the epoxy modification factor ψe equal 1.5 vs. 1.2?
ACI 318-19 §25.5.2.1 specifies ψe=1.5 when the bar is epoxy-coated and either the cover is less than 3db or the clear spacing between bars is less than 6db. These are the conditions where the coating penalty is harshest because splitting is more likely. Otherwise, for epoxy-coated bars with adequate cover and spacing, ψe=1.2. Regardless of the individual values of ψt and ψe, their product is capped at 1.7 by the code (§25.5.2.1, Table note), so the combined worst case never exceeds 1.7.
Does this calculator cover compression development length or lap splices?
No — this tool calculates tension development length only per §25.5. Compression development length (§25.5.5) uses a different formula: ldc = max(0.02fydb/(λ√f'c), 0.0003fydb), with a 8-in minimum. Tension lap splice lengths (§25.5.7) are Class A = 1.0ld or Class B = 1.3ld. Both are common follow-on calculations once ld is known.