Ideal Transformer
Compute ideal transformer secondary voltage, current, apparent power, and efficiency from turns ratio. Free online electrical engineering calculator with interactive charts.
About This Calculator
About the Ideal Transformer
An ideal transformer is a theoretical model that assumes perfect magnetic coupling, zero winding resistance, no core losses, and infinite core permeability. The fundamental relationships are governed by the turns ratio: Vp/Vs = Np/Ns = Is/Ip. Apparent power S = Vp x Ip = Vs x Is is perfectly conserved.
This calculator also models copper losses (I^2R losses) in the primary and secondary windings to demonstrate how winding resistance reduces efficiency from the ideal 100%. Enter Rp and Rs values to see the effect on real-world transformer performance.
Electrical engineers, students, and hobbyists use this calculator to quickly analyze transformer behavior for circuit design, power supply projects, and educational demonstrations. The step-down configuration (ratio > 1) converts high-voltage transmission levels to usable household voltages, while step-up configurations (ratio < 1) boost voltages for long-distance power transmission or specialized equipment.
For example, a transformer with 230 V primary, turns ratio of 2, and primary current of 5 A produces 115 V at 10 A on the secondary side with 1150 VA apparent power. Adding winding resistances of 0.5 Ω primary and 0.2 Ω secondary results in copper losses of 62.5 W, reducing efficiency from the ideal 100% to approximately 94.8%.
Key Formulas
- Secondary Voltage: Vs = Vp / (Np/Ns)
- Secondary Current: Is = Ip x (Np/Ns)
- Apparent Power: S = Vp x Ip (VA)
- Copper Losses: Pcu = Ip^2 x Rp + Is^2 x Rs
- Efficiency: η = Pout / (Pout + Pcu) x 100%
Regional Voltage Standards
India: 230V at 50Hz -- used across residential and commercial electrical distribution as per IS 12360.
United States: 120V at 60Hz -- standard household voltage per ANSI C84.1; 240V split-phase for large appliances.
United Kingdom: 230V at 50Hz -- harmonized European standard BS 7671 for all domestic supply.
Frequently Asked Questions
What is an ideal transformer?
An ideal transformer is a theoretical model with perfect magnetic coupling, zero winding resistance, no core losses, and infinite magnetic permeability. In practice, real transformers have small copper and core losses, but the ideal model provides accurate approximations for most design calculations.
How does the turns ratio affect voltage and current?
According to Vp/Vs = Np/Ns, the secondary voltage equals the primary voltage divided by the turns ratio. Simultaneously, Is/Ip = Np/Ns, so the secondary current equals the primary current multiplied by the turns ratio. A step-down transformer (Np > Ns) reduces voltage and increases current.
What is apparent power (VA) in a transformer?
Apparent power S = V x I measured in volt-amperes (VA) represents the total power flowing through the transformer. For an ideal transformer, input apparent power equals output apparent power (Vp x Ip = Vs x Is). Transformer ratings are typically given in VA or kVA.
What are the standard mains voltages in India, the US, and the UK?
India (IN): 230V at 50Hz. United States (US): 120V at 60Hz (split-phase, with 240V for large appliances). United Kingdom (UK): 230V at 50Hz. The calculator auto-detects your region and prefills these defaults.
Why does frequency not appear in these calculations?
For an ideal transformer operating under steady-state conditions, the turns-ratio voltage and current relationships are independent of frequency. Frequency affects core losses, magnetizing current, and skin effect in real transformers, but the ideal model isolates the fundamental winding ratio behavior.
How do copper losses affect transformer efficiency?
Copper losses (I^2R) occur in the primary and secondary windings due to wire resistance. Enter non-zero primary and secondary resistance values to see efficiency drop below 100%. At full load, copper losses dominate; at light load, core losses dominate in real transformers.
Can I use this calculator for both step-up and step-down transformers?
Yes. Enter a turns ratio greater than 1 for a step-down transformer (lower secondary voltage, higher secondary current) or less than 1 for a step-up transformer (higher secondary voltage, lower secondary current).
Is this calculator free to use?
Yes, the Ideal Transformer Calculator is completely free with no registration required. Results can be shared via URL, and the calculator automatically detects your regional voltage standards.