90° vs 45° Elbow
Same 1.5D centreline radius, half the turn. Where the tangent factor comes from, and why offsets are built from a pair of 45s.
- 90° centre-to-end
- A = 1.5 × NPS
- 45° centre-to-end
- B = 1.5 × NPS × tan 22.5°
- Tabulated B/A, NPS 4+
- 0.417
- Both
- Long radius, 1.5D centreline
Short answer. Both are long radius elbows turning on a 1.5 × NPS centreline radius; they differ only in how far around they go. The 45° elbow's centre-to-end dimension is geometrically the 90° figure times tan 22.5° ≈ 0.4142 — though B16.9 publishes rounded values, so the tabulated ratio is nearer 0.417 from NPS 4 up. Either way it is a little over four-tenths the length. Two 45° elbows produce a gentler, lower-loss offset than one 90°, which is why offsets and jog-arounds are usually built from a pair of 45s.
Where the tangent comes from
Centre-to-end is measured from the intersection of the two end centrelines to the welding end. For an elbow of centreline radius R turning through angle θ, that distance is R·tan(θ/2). At 90° the half-angle is 45°, tan 45° = 1, and the dimension is simply R = 1.5 × NPS. At 45° the half-angle is 22.5°, tan 22.5° = 0.4142, and the dimension shrinks accordingly.
Centre-to-end = R · tan(θ/2) · R = 1.5 × NPS for long radius
Dimensions are given in inches, with the millimetre equivalent beneath in grey.
| NPS | 90° centre-to-end A | 45° centre-to-end B | B / A |
|---|---|---|---|
| NPS 1/2 | 1.5038.10 mm | 0.6215.75 mm | 0.413 |
| NPS 3/4 | 1.1228.45 mm | 0.4411.18 mm | 0.393 |
| NPS 1 | 1.5038.10 mm | 0.8822.35 mm | 0.587 |
| NPS 1 1/4 | 1.8847.75 mm | 1.0025.40 mm | 0.532 |
| NPS 1 1/2 | 2.2557.15 mm | 1.1228.45 mm | 0.498 |
| NPS 2 | 3.0076.20 mm | 1.3835.05 mm | 0.460 |
| NPS 2 1/2 | 3.7595.25 mm | 1.7544.45 mm | 0.467 |
| NPS 3 | 4.50114.30 mm | 2.0050.80 mm | 0.444 |
| NPS 3 1/2 | 5.25133.35 mm | 2.2557.15 mm | 0.429 |
| NPS 4 | 6.00152.40 mm | 2.5063.50 mm | 0.417 |
| NPS 5 | 7.50190.50 mm | 3.1279.25 mm | 0.416 |
| NPS 6 | 9.00228.60 mm | 3.7595.25 mm | 0.417 |
| NPS 8 | 12.00304.80 mm | 5.00127.00 mm | 0.417 |
| NPS 10 | 15.00381.00 mm | 6.25158.75 mm | 0.417 |
| NPS 12 | 18.00457.20 mm | 7.50190.50 mm | 0.417 |
| NPS 14 | 21.00533.40 mm | 8.75222.25 mm | 0.417 |
| NPS 16 | 24.00609.60 mm | 10.00254.00 mm | 0.417 |
| NPS 18 | 27.00685.80 mm | 11.25285.75 mm | 0.417 |
| NPS 20 | 30.00762.00 mm | 12.50317.50 mm | 0.417 |
| NPS 22 | 33.00838.20 mm | 13.75349.25 mm | 0.417 |
| NPS 24 | 36.00914.40 mm | 15.00381.00 mm | 0.417 |
The geometry gives tan 22.5° = 0.4142, but the published dimensions are rounded, so the tabulated ratio settles near 0.417 from NPS 4 upward and departs from it in small bore. Always take the dimension from the table.
The table is not the formula
Worth noticing in the ratio column: the tabulated dimensions do not follow tan 22.5° exactly. From NPS 4 upward the ratio settles at about 0.417 — B16.9 rounds the published figures to convenient fractions rather than carrying the trigonometry through. Below that the departure is larger still; at NPS 1 the ratio is 0.587, because small-bore fittings are set by practical minimum dimensions rather than by the centreline radius rule. The formula explains where the dimensions came from; the table is what the fitting actually measures, and it is the table that governs a fabrication drawing.
Two 45s or one 90?
For a change of direction, one 90° elbow. For an offset — stepping the line sideways and continuing in the same direction — a pair of 45° elbows is almost always better. The flow turns twice through a gentler angle instead of twice through a sharp one, so the combined pressure loss is lower, and the offset distance can be tuned by varying the spool between them rather than being fixed by the fitting.
| Requirement | Use | Why |
|---|---|---|
| Change direction 90° | One 90° LR elbow | The direct solution; fewest welds. |
| Offset a line sideways | Two 45° elbows | Lower total pressure drop than two 90s, and the offset is adjustable by the spool length between them. |
| Route around an obstruction | Two 45° elbows | A gentler path with fewer flow disturbances for downstream instruments. |
| Enter a header at an angle | One 45° elbow | Reduces the turning loss into the header and keeps the branch geometry compact. |
| Upstream of a flow meter | Fewest fittings possible | Every elbow distorts the profile; meters specify straight run in pipe diameters, so 45s help but do not substitute. |
Dimensions: 90° long radius elbow · 45° long radius elbow · LR vs SR · all B16.9 fittings.
Common questions
How do I calculate the centre-to-end of a 45° elbow?
The geometry is B = 1.5 × NPS × tan 22.5° = 1.5 × NPS × 0.4142, but ASME B16.9 publishes rounded dimensions, so read the tabulated value rather than computing it. NPS 6 is 3.75 in, not the 3.73 in the formula gives.
Is a 45° elbow shorter than a 90° elbow?
Yes — the centre-to-end dimension is about 0.417 times the 90° figure in NPS 4 and above, a little over four-tenths, because the fitting turns through half the angle.
Do two 45° elbows have less pressure drop than one 90°?
For an offset, yes. Two gentle turns lose less than one sharp turn plus the recovery behind it, and the flow leaves the pair with a less distorted profile.
Do 45° elbows come in short radius?
ASME B16.9 does not tabulate a short radius 45° elbow. Short radius is published for the 90° elbow only.