How to use the thickness calculator
- Pick what to calculate, then the length unit (mm or in) and the velocity unit (m/s or in/µs). Times are always in microseconds (µs).
- Enter the velocity of the wave the gauge times, which is longitudinal for a contact or dual-element thickness probe, or pick a material preset as a starting point.
- Enter the round-trip transit time and, if you know it, the zero offset. Leave the zero at 0 to see the textbook form T = V × t ÷ 2.
- For a calibration, enter two blocks of the same material with known thicknesses and the transit time measured on each.
The formulas and who prints them
- Thickness: T = V × t ÷ 2. Equation 4 of the Olympus/Evident Technical Notes (p. 3), from the velocity and the round-trip time of flight. Evident's thickness gauge tutorial writes the same relation as T = (V) × (t/2).
- With a zero offset: T = V × (t − t0) ÷ 2. The tutorial says a zero offset is subtracted in some cases for fixed instrument and sound-path delays.
- Velocity: V = 2 × T ÷ (t − t0) and time: t = 2 × T ÷ V + t0 are the same relation rearranged.
- Two-point calibration: V = 2 × (T2 − T1) ÷ (t2 − t1), then t0 = t1 − 2 × T1 ÷ V. Two known thicknesses and their two times give two equations, and the two unknowns are the velocity and the zero. This is the "two-point calibration" Evident recommends, which also asks for blocks 2:1 or more apart in thickness, with 5:1 or more optimum.
- Wrong velocity: T true = T read × V true ÷ V set. The transit time does not change, so the reading scales with the velocity entered.
Unit factors: 1 m/s = 0.001 mm/µs, and 1 in = 25.4 mm exactly (NIST), so 1 in/µs = 25.4 mm/µs = 25,400 m/s.
Worked example 1: thickness from a transit time
Invented numbers. Steel at 5,890 m/s (5.89 mm/µs) with a round-trip time of 8.50 µs and no zero offset: T = 5.89 × 8.50 ÷ 2 = 25.0325 mm. With a 0.20 µs zero offset the time in the part is 8.30 µs and T = 5.89 × 8.30 ÷ 2 = 24.4435 mm. Forgetting the zero here overstates the wall by about 0.59 mm.
Worked example 2: two-point velocity and zero calibration
Invented numbers. A 5.00 mm block reads 1.90 µs and a 25.00 mm block of the same material reads 8.70 µs. V = 2 × (25.00 − 5.00) ÷ (8.70 − 1.90) = 40 ÷ 6.80 = 5.8824 mm/µs (5,882.4 m/s). Zero t0 = 1.90 − 2 × 5.00 ÷ 5.8824 = 1.90 − 1.70 = 0.20 µs. The blocks are 5:1 apart. Check the calibration on a third block whose thickness lies between the two.
Worked example 3: a reading taken at the wrong velocity
Invented numbers. A gauge left at 5,890 m/s reads 12.00 mm on a part whose velocity is 5,660 m/s. T true = 12.00 × 5,660 ÷ 5,890 = 11.5314 mm, so the reading was about 4.06% high. A slower part takes longer to cross, and a gauge set too fast turns that longer time into too much thickness.
These are original arithmetic examples, not exam questions. More of the same arithmetic is in the UT Level II formulas guide and the NDT math drill.
Common mistakes
- Not halving the time. The measured time is a round trip. Using it whole doubles the thickness.
- Using the shear velocity. A straight-beam thickness reading uses the longitudinal velocity; see shear wave vs longitudinal wave.
- Mixing units. m/s times µs is not mm. Convert to mm/µs (divide m/s by 1,000) before you multiply.
- Reading the error wrong. Evident notes that an error growing with thickness points to the velocity, and an error of a fixed amount on several steps points to the zero.
- Calibrating on the wrong material. Velocity changes with alloy, grain structure and temperature, so the presets below are a start, not a calibration.
- Very thin walls. Near the surface the echo can be lost in the initial pulse; see dead zone. The couplant layer is part of the zero; see couplant.
Ultrasonic thickness questions
Why does the thickness formula divide by 2?
The gauge times the sound from the probe to the back wall and back again. That round trip covers the thickness twice, so thickness = velocity × time ÷ 2. Evident's thickness gauge tutorial writes it as T = (V) × (t/2).
What is the zero offset in a thickness reading?
It is the part of the measured time that is not sound travelling in the part: instrument and cable delays, the probe's wearplate or delay line, and the couplant. The gauge subtracts it before halving the time. A two-point calibration on two blocks of known thickness finds both the velocity and the zero offset.
Can I use these numbers for a real thickness reading?
No. Real thickness readings follow your written procedure, a calibration on the material being measured and a qualified person. This page shows the arithmetic and does not accept or reject any reading or set a minimum thickness.
Related tools: the UT beam calculator for near field and beam spread, and the acoustic impedance calculator for how much sound crosses the couplant and the back wall.