Transformer Turns Ratio Calculator
Primary V + secondary V → turns ratio. Also computes secondary current and reflected impedance.
Result
- Primary voltage Vp120 V
- Secondary voltage Vs12 V
- Turns ratio Np/Ns10.0000
- Primary current Ip0.5 A
- Ideal secondary current IsFrom Ip × n (ideal — assumes 100% efficiency)5.000 A
- Reflected primary impedanceZl seen from the primary side = n² · Zl800.00 Ω
- Is computed from ZlFrom Vs / Zl1.500 A
- Ip needed for that IsFrom Is / n (ideal)0.150 A
Step-by-step
- Turns ratio: n = Np/Ns = Vp/Vs = 120 / 12 = 10.0000.
- Ideal current law: Is = Ip × n = 0.5 × 10.0000 = 5.0000 A.
- Reflected impedance: Z_primary = n² × Zl = 100.0000 × 8 = 800.0000 Ω.
How to use this calculator
- Enter primary and secondary voltages.
- Optionally enter primary current to see the ideal secondary current.
- Optionally enter secondary load impedance to see the reflected primary impedance.
About this calculator
An ideal transformer obeys Vp/Vs = Np/Ns and Ip/Is = Ns/Np = 1/n, with power conserved: Vp·Ip = Vs·Is. The same physical relationship makes impedances reflect between the primary and secondary sides scaled by n²: a load Zl on the secondary appears as n²·Zl on the primary. Real transformers have ~95-99% efficiency and additional leakage inductance, but for sizing and matching purposes the ideal-transformer equations are accurate within a few percent.
What this calculator does
This calculator reports the turns ratio n = Np/Ns = Vp/Vs of an ideal transformer along with the secondary current that the ideal-transformer current law (Is = Ip · n) predicts, and the impedance reflected from secondary to primary (Z_primary = n² · Zl). It also cross-checks by computing Is from Vs/Zl and the corresponding Ip — useful for sizing the primary fuse or breaker on a known secondary load.
How it works — the formula
Np / Ns = Vp / Vs = n
Is / Ip = n (ideal)
Z_primary = n² · Z_secondary
P_in = P_out (ideal): Vp · Ip = Vs · IsFaraday's law gives Vp/Vs = Np/Ns for the voltage relationship. Energy conservation (P_in = P_out for an ideal transformer) gives the inverse current relationship. The impedance-reflection identity follows directly: Z = V/I, so Z scales by n × n = n² when both V and I change by factors of n in opposite directions.
Worked examples
- Inputs:
- Vp=120, Vs=12, Ip=0.5, Zl=8
- Output:
- n = 10:1; Is = 5 A; Z_primary = 800 Ω
Classic step-down for low-voltage lighting.
- Inputs:
- Vp=6, Vs=120, Ip=20, Zl=240
- Output:
- n = 0.05 (1:20); Is = 1 A; Z_primary = 0.6 Ω
Step-up — primary sees the load reflected at 1/400 of its actual value.
- Inputs:
- Vp=160, Vs=8, Ip=0.1, Zl=8
- Output:
- n = 20:1; Is = 2 A; Z_primary = 3200 Ω
Output transformer matches a 3.2 kΩ tube plate impedance to an 8 Ω speaker.
When to use this vs other tools
Use this for power and audio transformer sizing. For pulse / flyback / switch-mode transformers the duty-cycle and inductance specs matter more than turns ratio alone.
- Ohm's Law
Use after determining secondary V and load Zl to find Is = Vs / Zl directly.
- Power (Watts)
Use to verify P_in ≈ P_out for sanity-checking transformer specs.
- Audio Impedance
Use when an audio transformer matches a high-impedance source to a low-impedance load (or vice versa).
- Voltage Drop
Use to size primary-side conductors based on the higher primary current of step-up arrangements.
Authority note
IEC 60076 is the international standard for power-transformer specifications; IEEE C57 is the corresponding US/IEEE standard family. The turns-ratio and impedance-reflection identities used here are textbook Faraday-law derivations that appear identically in both standard families.
Limitations
- Ideal-transformer model — real transformers have leakage inductance, winding resistance, and core losses (~1-5% combined).
- Assumes AC operation; DC voltages cannot pass through a transformer.
- Saturation: applying too much voltage at low frequency drives the core into saturation, collapsing inductance and current-limiting.
- Frequency: power transformers are sized for 50/60 Hz; audio output transformers extend to ~20 kHz; SMPS transformers operate ~50-500 kHz with different design rules.
Transformer design for mains-voltage applications requires safety isolation, thermal margin, and certification (UL/CE/CSA). Use ready-made transformers from reputable manufacturers for any installation that connects to the grid.