Development Length (Ld) Calculator
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Pick the bar diameter, concrete grade and steel grade, and get the development length Ld in mm and as a multiple of the bar diameter — for tension or compression, straight from IS 456.
Development Length (Ld) Calculator — IS 456
Ld = φ·σs ⁄ 4τbd · deformed bars ×1.6 · compression ×1.25
Bar anchored in concrete
Ld = 752 mm ≈ 47φ
For deformed (TMT/HYSD) bars τbd is raised 60%; compression adds another 25%. σs = 0.87·fy.
Development length
752 mm
16 mm, M20, Fe 415, tension · ≈ 47φ
Ld
752 mm
As a multiple
47φ
τbd (design bond)
1.92 N/mm²
σs = 0.87 fy
361 N/mm²
Ld for every diameter · M20, Fe 415, tension
6 mm
282 mm
47φ
8 mm
376 mm
47φ
10 mm
470 mm
47φ
12 mm
564 mm
47φ
16 mm
752 mm
47φ
20 mm
940 mm
47φ
25 mm
1,175 mm
47φ
32 mm
1,504 mm
47φ
Provide at least this embedment past the point where the bar is fully stressed, or anchor the balance in a standard hook/bend. A 90° bend counts as 8φ of anchorage, a 135° hook as 16φ. Where the splice can't fit, lap the bars — see the lap length calculator.
The formula (IS 456, cl 26.2.1)
Ld = (φ × σs) ÷ (4 × τbd)
- φ = bar diameter, σs = stress in the bar = 0.87·fy for a fully-stressed bar.
- τbd = design bond stress. For plain bars in tension it is 1.2 (M20), 1.4 (M25), 1.5 (M30), 1.7 (M35), 1.9 (M40). For deformed (TMT/HYSD) bars it is raised 60% (×1.6); for bars in compression, a further 25% (×1.25).
Worked example
A 16 mm Fe415 bar in M20 concrete, in tension:
- τbd = 1.2 × 1.6 = 1.92 N/mm², σs = 0.87 × 415 = 361 N/mm²
- Ld = 16 × 361 ÷ (4 × 1.92) = 752 mm ≈ 47φ
- In compression τbd rises 25%, so Ld drops to 602 mm ≈ 38φ
Ld as a multiple of φ (deformed bars, Fe415)
| Grade | τbd | Tension Ld | Compression Ld |
|---|---|---|---|
| M20 | 1.92 | 47φ | 38φ |
| M25 | 2.24 | 40φ | 32φ |
| M30 | 2.40 | 38φ | 30φ |
For Fe500 the values are ~20% higher (M20 tension ≈ 57φ). Multiply φ by the factor for a quick field number.
Frequently asked questions
What is development length in simple terms? The length a bar must be embedded in concrete so bond can transfer its full force before it is needed — any shorter and the bar can slip before it yields.
What is the development length of a 16 mm bar? For Fe415 in M20, about 752 mm (47φ) in tension, or 602 mm (38φ) in compression. It rises with steel grade and falls as concrete grade rises.
Why is development length lower in compression? IS 456 allows a 25% higher bond stress for bars in compression, so the required embedment is about 20% shorter than in tension.
What is the 47d / 40d thumb rule? For Fe415, tension Ld works out to about 47φ in M20 and 40φ in M25 — the "47d" and "40d" numbers site engineers quote. They are the formula above, not separate rules.
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CivilSite Editorial Team✓ Engineer reviewed
Written and reviewed by practising civil engineers with 10+ years of Indian residential construction experience.