Ideal Transformer Calculator — Voltage, Current & Turns Ratio | Vs = Vp × (Ns/Np)

How Does an Ideal Transformer Work?

An ideal transformer is a theoretical model that transfers electrical energy between two circuits with 100% efficiency — no winding resistance, no core losses, no leakage flux. While real transformers always have some losses, the ideal transformer is the essential starting point for understanding voltage and current transformation in AC circuits.

The Two Core Equations

Everything in an ideal transformer follows from the turns ratio k = N_s / N_p. Two equations govern how voltage and current transform:

• Voltage equation: V_s = V_p × (N_s / N_p)
  The secondary voltage is directly proportional to the number of secondary turns. More turns on the secondary side → higher output voltage.
• Current equation: I_s = I_p × (N_p / N_s)
  The secondary current is inversely proportional to the turns ratio. When voltage increases, current decreases by the same factor — keeping power constant.
• Power conservation: P_p = P_s, so V_p × I_p = V_s × I_s
  In an ideal transformer, all input power appears at the output with zero loss.

Types of Transformers

• Step-Up Transformer (k > 1, N_s > N_p) — increases voltage, decreases current proportionally. Used in power generation plants to raise voltage to hundreds of kilovolts for efficient long-distance transmission.
• Step-Down Transformer (k < 1, N_s < N_p) — decreases voltage, increases current. Used to convert high-voltage power line voltage (e.g., 11,000 V or 110 kV) to household voltage (110 V in the USA, 220 V in Europe and most of the world).
• Isolation Transformer (k = 1, N_s = N_p) — maintains the same voltage but provides galvanic isolation between primary and secondary circuits, improving safety and reducing electrical noise.

How Does a Transformer Work Physically?

A transformer consists of two coils — primary and secondary — wound around a common ferromagnetic core. An alternating current (AC) in the primary coil creates a rapidly changing magnetic field in the core. By Faraday's Law of Induction, this changing magnetic flux induces an electromotive force (EMF) in the secondary coil.

The key insight is that the induced voltage depends on the number of turns that the magnetic flux passes through. A secondary coil with more turns intercepts more of the changing flux and therefore produces a proportionally higher voltage.

Note that transformers only work with AC (alternating current). A steady DC current creates a static magnetic field that does not induce any voltage in the secondary coil.

Current Transformer vs Voltage Transformer

• Voltage Transformer (VT / PT) — designed to step voltage up or down accurately while keeping the turns ratio precise. Used in power supplies and metering applications.
• Current Transformer (CT) — has many turns on the primary side and few on the secondary. Converts large primary currents (hundreds or thousands of amperes) to a small, safe, measurable secondary current (typically 5 A or 1 A) for metering, protection relays, and instrumentation.

Practical Examples

• Power grid: A generator produces electricity at ~20 kV. Step-up transformers raise it to 110–765 kV for long-distance transmission, then step-down transformers reduce it to 110 V (USA/Canada) or 220–240 V (Europe, Russia, most of the world) for homes and businesses.
• Phone charger: A small transformer (or switching power supply) inside converts 110 V / 220 V AC to 5–20 V for charging. The turns ratio is roughly 1:20 to 1:44.
• Audio equipment: Audio transformers match impedances between amplifier stages (e.g., 600 Ω to 8 Ω for speaker matching) to maximize power transfer.
• Welding machines: Industrial step-down transformers provide high current at low voltage (e.g., 50–300 A at 20–80 V) for arc welding from a standard 220 V or 380 V supply.
• Medical equipment: Isolation transformers in hospitals protect patients from electric shock by isolating medical devices from the mains earth ground.

Unit Systems in This Calculator

Electrical quantities — volts, amperes, and watts — use the same SI units in both the metric and American measurement systems. This calculator lets you enter values in millivolts (mV), volts (V), or kilovolts (kV) for voltage, and in milliamperes (mA), amperes (A), or kiloamperes (kA) for current. Results are automatically scaled and displayed in the most readable unit prefix.

Ideal vs Real Transformer

Real transformers differ from the ideal model in several ways:

• Winding resistance (copper losses) — causes a voltage drop and generates heat proportional to I²R.
• Core losses — hysteresis and eddy current losses in the iron core, proportional to frequency and flux density.
• Leakage flux — not all magnetic flux from the primary passes through the secondary, reducing coupling efficiency.
• Magnetising current — a real transformer draws a small no-load current to maintain the core magnetic field.

Despite these differences, the ideal transformer equations provide an excellent first approximation and are used as the foundation for all transformer design and analysis.