Angle Beam
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UT skip-distance calculator: angle beam, full and half skip

Find the surface distance and sound path for a refracted angle beam in a flat plate. Locate a reading on the first or second leg and explore how wedge velocity changes the beam angle.

Method checked against Evident, An Introduction to Ultrasonic Flaw Detection on 17 Oct 2026. A calculation aid for study and estimating, not a substitute for the listed equipment's documentation or the AHJ.

Calculate the beam path

Results update as you type. All angles are measured from the surface normal.

Distances at 60°

Half skip · surface distance
43.3013 mm
Full skip · surface distance
86.6025 mm
Half-skip sound path · one leg
50 mm
Full-skip sound path · V-path
100 mm

Reading position: leg 2

Depth below entry surface: 12.5 mm.
Surface distance from beam entry: 64.9519 mm.

Depth = 2T − SP × cos θ. The exact backwall point is assigned to leg 1; the full-skip endpoint is assigned to leg 2.

Angle beam path through a flat plateBeam at 60 degrees from normal travels down on leg 1, reflects at the backwall, and returns to the top on leg 2. Thickness 25 mm, full skip 86.6025 mm. Reading on leg 2: depth 12.5 mm, surface distance 64.9519 mm.Entry → full skip: 86.6025 mmθ = 60° from normal (dashed)Backwall · T = 25 mm
Leg 1: entry to backwall. Leg 2: backwall to top. The outlined marker shows the sound-path reading. The plate and beam use the same scale; extreme angles can flatten or narrow the drawing.

Formulas and the two legs

T is plate thickness; θ is the refracted angle from the normal inside the test material. SP is the accumulated one-way sound path from the beam entry point to the reflector. Lengths use one consistent unit. The V-path follows both legs to the next top-surface intersection; it is not the round-trip echo distance back to the probe.

  • Half skip (surface distance) = T × tan θ.
  • Full skip (surface distance) = 2T × tan θ.
  • Half-skip sound path = T / cos θ.
  • Full-skip sound path (V-path) = 2T / cos θ.
  • Surface distance for a reading = SP × sin θ.
  • Leg 1 depth = SP × cos θ, for 0 ≤ SP ≤ T / cos θ.
  • Leg 2 depth = 2T − SP × cos θ, for T / cos θ < SP ≤ 2T / cos θ.

These are right-triangle derivations using the equal-angle reflection geometry described in Evident's An Introduction to Ultrasonic Flaw Detection. For leg 2, the beam has already crossed the thickness T; its upward travel is SP × cos θ − T. Subtract that upward travel from T to get 2T − SP × cos θ.

Worked example: 25 mm plate at 60°

Half skip = 25 × tan 60° = 43.3013 mm; full skip = 86.6025 mm. One leg is 25 / cos 60° = 50 mm; the V-path is 100 mm.

A 75 mm sound-path reading lies on leg 2 because 50 < 75 ≤ 100. Its surface distance is 75 × sin 60° = 64.9519 mm. Its depth is 2 × 25 − 75 × cos 60° = 12.5 mm below the top surface. Applying the leg 1 formula here would incorrectly place the reflector below the backwall.

Snell's law and critical angles

For an incident longitudinal wave in the wedge and a refracted shear wave in the plate, sin α / cW = sin θ / cS. Rearranging gives θ = arcsin[(cS / cW) × sin α]. Here α is the incident angle from normal, cW is wedge longitudinal velocity, cS is material shear velocity, and cL is material longitudinal velocity. The calculator substitutes your numbers above.

At a critical angle the relevant refracted ray reaches 90°. Setting its sine to 1 gives αc1 = arcsin(cW / cL) for the first (longitudinal) critical angle and αc2 = arcsin(cW / cS) for the second (shear) critical angle. A ratio greater than 1 means that critical angle does not exist for the entered velocities. At or beyond the second critical angle, this tool suppresses the through-thickness shear-path results.

Source: Evident, Ultrasonic Flaw Detection Tutorial: 2.5 Wave Front Dynamics. This is a ray model; it does not calculate beam spread, transmission amplitudes or surface-wave paths.

Assumptions and use limits

Use a flat, parallel-sided plate with a uniform, isotropic velocity and a calibrated angle and beam index point. This tool supports only the first two legs. Curved surfaces, anisotropy and mode conversion at reflections need a different model. Reference velocities are starting values, not a calibration: confirm the material, temperature and actual wedge velocity against your procedure.