The above formula is valid for a single phase transformer
For three phase transformer single phase voltage ratio is not equal to 3 phase voltage ratio, why? because you need to consider the primary and secondary winding configuration. For delta to wye the multiplying factor for single phase voltage ratio is 1.732 [67/13.75*1.732 = 8.439] to get the calculated three phase voltage ratio as shown by the above circuit model. Modern turn ratio test instrument are using software lookup table to find the correct multiplying factor that correspond to the specified winding configuration entered during transformer TTR testing session. So make sure that the TTR test instrument winding configuration setting is the same with the transformer winding configuration.
It is a good practice to review the TTR test instrument winding configuration setting and make sure it is the same with the transformer winding configuration shown on the transformer nameplate. Factory test report calculated value for three phase transformer voltage ratio can be evaluated using single phase voltage ratio multiplied by a factor based on winding configuration. Shown below are the single phase multiplying factor based on transformer winding connection to convert line to phase voltage or current.
Application of lesson learned:
Given a Δ  Y, Dyn1 (IEC vector code) group 2, angular displacement is 30° (IEEE C57.12.70 ), 3 phase transformer with primary voltage 67 kV and Secondary voltage 13.75 kV, secondary neutral, X0 was brought out; Calculate the 3 phase voltage ratio
Valid for 3 Φ , Δ  Y only
You need to multiply the delta voltage by 1.732. It comes from wyeconnection on secondary winding.
voltage ratio, " a "

= 
kV Primary Voltage * 1.732
kV Secondary Voltage

Use your voice to enter data
Calculator 1
If your primary winding is shorted, you will expect to have a lower turn ratio (a) in your TTR measurement compare to factory test report. It is also indicated by lower primary voltage reading. Use the calculator below to do simulation.
Valid for 3 Φ , Δ  Y only
Given three phase turn ratio 8.4396 and Secondary voltage 13.75 kV; Calculate the primary voltage
three phase turn ratio, a

= 
kV Primary Voltage *1.732
kV Secondary Voltage

Use your voice to enter data
Calculator 2
If your secondary winding is shorted, you will expect to have a higher turn ratio (a) in your TTR measurement compare to factory test report. It is also indicated by lower secondary voltage reading. Use the calculator below to do simulation.
Valid for 3 Φ , Δ  Y only
Given a three phase turn ratio 8.4396 and Primary voltage 67 kV; Calculate the secondary voltage
three phase turn ratio, a

= 
kV * 1.732 Primary Voltage
kV Secondary Voltage

Use your voice to enter data
Calculator 3
Valid for 1 Φ only
Given single phase voltage ratio 4.8727 and Secondary voltage 13.75 kV; Calculate the primary voltage
single phase voltage ratio, a

= 
kV Primary Voltage
kV Secondary Voltage

Use your voice to enter data
Calculator 4
Valid for 1 Φ only
Given a single phase turn ratio 5.5333 and Primary voltage 69 kV; Calculate the secondary voltage
Turn Ratio, a

= 
kV Primary Voltage
kV
Secondary Voltage

Use your voice to enter data
Calculator 5
Valid for 1 Φ only
Given primary coils number of turns = 498 and secondary number of turns = 90; Calculate the turn ratio
Single phase turn ratio, a

= 
Primary Coils
Secondary Coils

Use your voice to enter data
Calculator 6
Valid for 1 Φ only
Given single phase turn ratio = 5.5333 and secondary number of turns = 90; Calculate the primary number of turns of coil
single phase turn Ratio, a

= 
Primary Coils
Secondary Coils

Use your voice to enter data
Calculator 7
Valid for 1 Φ only
Given single phase turn ratio = 5.5333 and primary number of turns = 498; Calculate the secondary number of turns of coil
single phase turn ratio, a

= 
Primary Coils
Secondary Coils

Use your voice to enter data
Calculator 8
Valid for 1 Φ only
Given secondary FLA = 1296.41 and primary FLA = 234.29; Calculate the single phase turn ratio
single phase turn ratio, a

= 
A, Secondary current
A, Primary current

Use your voice to enter data
Calculator 9
Valid for 1 Φ only
Given single phase turn ratio = 5.5334 and primary FLA = 234.29; Calculate the secondary FLA
single phase turn ratio, a

= 
Secondary current
Primary current

Use your voice to enter data
Calculator 10
Valid for 1 Φ only
Given single phase turn ratio = 5.5334 and secondary FLA = 1296.41; Calculate the primary FLA
single phase turn ratio, a

= 
Secondary current
Primary current

Use your voice to enter data
Calculator 11
Given 3 Phase MVA rating = 28 and secondary voltage = 69 kV; Calculate the primary FLA
3 Phase MVA RATED POWER TRANSFORMER
primary, Amp

= 
3 Phase MVA Rating
Primary kV * 1.732

Use your voice to enter data
Calculator 12
Given secondary FLA = 1296.41 and secondary voltage = 12.47 kV; Calculate the MVA rating of transformer
secondary, Amp

= 
3 Phase MVA Rating
Secondary kV * 1.732

Use your voice to enter data
Calculator 13
Given 3 phase kVA = 1000 and primary voltage = 480; Calculate the primary FLA
3 Phase KVA RATED POWER TRANSFORMER
primary, Amp

= 
3 Phase kVA Rating
Primary V * 1.732

Use your voice to enter data
Calculator 14
Given secondary FLA = 2405.70 and secondary voltage = 240; Calculate the kVA rating of transformer
secondary, Amp

= 
3 Phase kVA Rating
Secondary V * 1.732

Use your voice to enter data
Calculator 15
Given primary FLA = 1202.85 and 3 phase kVA = 1000; Calculate the primary voltage
primary, Amp

= 
3 Phase kVA Rating
Primary V * 1.732

Use your voice to enter data
Calculator 16