90 Degree Mitered Corner Converter
Calculate the effective electrical length of a 90-degree mitered corner in a PCB transmission line from the conductor width and height. Enter the trace dimensions in mm to get the extra length added by the chamfered bend.
Mitered Corner Length Estimator
90 Degree Mitered Corner Formula
Where:
- \(x\) — effective length of the mitered corner (mm)
- \(w\) — conductor width at the corner (mm)
- \(h\) — conductor height at the corner (mm)
This empirical formula, widely used in microwave PCB design, estimates the electrical length a chamfered 90-degree bend contributes to a transmission line. The compensation depends only on the aspect ratio \(h/w\): as the conductor becomes relatively taller, the exponential term shrinks and the effective length approaches \(1.04\,w\).
90 Degree Mitered Corner – Calculation Example
Example: a microstrip trace makes a 90-degree mitered turn. The conductor is \(w = 5\) mm wide and \(h = 1.5\) mm high at the corner.
\[ x = 5 \cdot \left( 1.04 + 1.30 \, e^{-1.35 \cdot \frac{1.5}{5}} \right) \]
\[ x = 5 \cdot \left( 1.04 + 1.30 \, e^{-0.405} \right) = 5 \cdot (1.04 + 1.30 \cdot 0.667) \]
\[ x = 5 \cdot 1.907 = 9.535 \text{ mm} \]
Result: the mitered corner has an effective length of approximately 9.54 mm, which should be counted as part of the line's electrical path.
How to Use the Calculator
- Enter the Conductor width (\(w\)) in millimeters — the width of the trace as it passes through the corner.
- Enter the Conductor height (\(h\)) in millimeters — the vertical extent of the conductor at the bend.
- Read the Effective Length in mm. This is the electrical length contributed by the mitered 90-degree corner.
What Is a 90 Degree Mitered Corner?
In high-frequency PCB design, a transmission line rarely runs in a perfectly straight line from source to load. When a microstrip or stripline trace changes direction, the geometry of the bend itself disturbs the fields around the conductor. A sharp, unmitered 90-degree corner adds excess capacitance at the outer edge of the bend, causing impedance discontinuities, signal reflections, and degraded return loss — problems that grow more severe as frequency increases.
The standard fix is to miter (chamfer) the corner: a triangular portion of the outer edge is cut away so the bend looks like a diagonal shortcut rather than a sharp elbow. Removing this material reduces the excess capacitance and brings the local impedance back close to the characteristic impedance of the line. A properly mitered corner behaves almost like a short, uniform section of straight line.
That short "equivalent section" is exactly what this calculator computes. The mitered bend does not have zero length — electrically, it behaves as an extra segment of line of length \(x\), given by the empirical formula above. When you need to know the total electrical length of a routed line — for phase matching, quarter-wave transformers, resonators, filters, or distributed matching networks — you must add the effective length of every bend to the sum of the straight segments.
The result scales with conductor width \(w\), so wide, low-impedance lines (which store more charge at a corner) incur more effective length than narrow ones. The \(h/w\) ratio modulates this: taller conductors relative to their width reduce the added length toward the asymptotic minimum of \(1.04\,w\). For more on how line geometry determines characteristic impedance, see the Microstrip PCB Impedance and Stripline Impedance calculators.
Assumptions and Practical Tips
- Empirical model: the formula is a curve fit from measured and simulated data for typical PCB transmission lines. It gives a good engineering estimate, not an exact solution; for critical designs at very high frequencies, verify with a full-wave EM simulator or measured S-parameters.
- Moderate aspect ratios: the fit is most reliable for ordinary trace geometries. Extreme \(h/w\) values (very tall or very flat conductors) push the model outside the range it was derived for.
- Consistent units: the formula is dimensionally homogeneous in \(x\), \(w\), and \(h\), so it works in any unit system — but the calculator expects millimeters, and the result comes back in millimeters.
- Two bends, two corrections: if a route has multiple 90-degree turns, compute the effective length for each corner and add all of them to the straight-segment total.
- Corners interact: the model assumes an isolated bend. If two corners are placed closer than a few line widths apart, their fields couple and the simple per-corner correction becomes less accurate — relevant when routing dense layouts, a situation also covered in the PCB Microstrip Crosstalk calculator.
- Not a miter-cut calculator: this tool returns the electrical length of the corner, not the physical size of the chamfer to cut. Typical miter designs remove roughly 50–70% of the corner diagonal, but the exact chamfer fraction for a given line is a separate design decision.
Quick Reference Values
For a quick sanity check, the effective length is between \(1.04\,w\) (very tall conductors, \(h/w \gtrsim 2\)) and about \(2.34\,w\) (flat conductors, \(h \to 0\)). For the common case \(h = w/2\), the corner contributes roughly \(1.62\,w\).
Frequently Asked Questions
How do I calculate the mitered corner length by hand without the calculator?
First find the aspect ratio \(h/w\). Multiply it by \(-1.35\) and raise \(e\) to that power (on a scientific calculator use the \(e^x\) key; e.g. \(e^{-0.405} \approx 0.667\)). Then plug into \(x = w(1.04 + 1.30 e^{-1.35 h/w})\). The exponential term is always between 0 and 1.30, so you can sanity-check that your result falls between \(1.04w\) and \(2.34w\).
Can I use mils or inches instead of millimeters?
The formula is dimensionally consistent, so it works in any length unit as long as \(w\) and \(h\) use the same unit — the result then comes out in that unit. This calculator, however, expects millimeters. To convert from mils, remember \(1 \text{ mil} = 0.0254\) mm; a 10-mil trace is 0.254 mm. Mixing units (mils for width, mm for height) is a common error that produces meaningless aspect ratios.
How do I convert the effective length into electrical degrees or phase delay?
Convert the physical length \(x\) to electrical length using the guided wavelength: \(\theta = 360° \cdot x/\lambda_g\). For microstrip, find \(\lambda_g = c/(f\sqrt{\varepsilon_{eff}})\) with the effective dielectric constant of your stackup. For example, if \(\lambda_g = 60\) mm at your frequency, a 9.54 mm corner adds about \(57°\) of phase — significant for impedance matching and phase-critical routing.
What happens if the conductor height is zero or very large?
With \(h = 0\) the exponential term equals 1, giving the maximum effective length of \(2.34w\). As \(h/w\) grows past about 2, the exponential term decays toward zero and \(x\) asymptotically approaches \(1.04w\). Note that the empirical fit was derived for ordinary trace geometries, so results at extreme aspect ratios should be treated as rough estimates and verified with an EM simulator if the design is critical.
Does this formula work for striplines, coplanar waveguides, or round conductors?
The formula was curve-fitted for typical PCB transmission lines — primarily microstrip-like geometries — where \(w\) is the trace width and \(h\) the conductor height at the bend. Applying it unchanged to very different structures (round wire, coax-like transitions, heavily coupled coplanar waveguide) can misestimate the corner's electrical length. For non-standard cross-sections at high frequency, treat the result as a first approximation and verify with field simulation or measurement.
How do I count corners in a route with multiple 90-degree bends?
Compute the effective length for each bend separately — bends of different widths give different corrections — then add every value to the total straight-segment length. Be careful with closely spaced corners: if two bends sit within a few trace widths of each other, their fields interact and the simple per-corner sum loses accuracy. In dense layouts, either space the bends farther apart or validate the combined section with a full-wave simulator.
Can I use this calculator for an unmited (sharp) 90-degree bend?
No. The formula estimates the electrical length of a properly mitered bend, where the chamfer has already compensated most of the corner's excess capacitance. A sharp, square corner behaves differently — it introduces a larger impedance discontinuity and more reflection, and its equivalent circuit cannot be represented by this simple extra-length model. Miter the bend first (typically cutting 50–70% of the corner diagonal), then use this calculator.