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Transformer Turns Ratio Calculator

Relate voltage to turns ratio in a transformer.

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Primary Voltage

Formula first

Overview

The transformer turns ratio equation defines the proportional relationship between the voltages across the primary and secondary coils and the number of wire loops in each winding. It describes how magnetic induction allows for the modification of alternating current voltage levels while maintaining the frequency of the electrical signal.

Symbols

Variables

V = Primary Voltage, V = Secondary Voltage, Np = Primary Turns, Ns = Secondary Turns, Voltage Ratio = Voltage Ratio

Primary Voltage
Secondary Voltage
Primary Turns
Secondary Turns
Voltage Ratio

Apply it well

When To Use

When to use: Apply this formula when analyzing ideal transformers where energy loss through heat or flux leakage is assumed to be zero. It is used specifically for alternating current (AC) systems to determine how many turns of wire are needed to achieve a target output voltage.

Why it matters: This principle is fundamental to the global power grid, enabling high-voltage transmission over long distances to reduce energy loss before stepping the voltage down for safe consumer use. It allows electronic devices to operate at low, safe voltages even when plugged into high-voltage wall outlets.

Avoid these traps

Common Mistakes

  • Swapping primary and secondary.
  • Forgetting ratio direction.

One free problem

Practice Problem

A step-down transformer is used to reduce a household voltage of 120V to power a small device at 6V. If the primary coil has 400 turns, how many turns are in the secondary coil?

Primary Voltage120
Secondary Voltage6
Primary Turns400

Solve for:

Hint: The ratio of primary to secondary voltage must equal the ratio of primary to secondary turns.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Halliday, Resnick, and Walker, Fundamentals of Physics
  2. Wikipedia: Transformer
  3. Halliday, Resnick, Walker, Fundamentals of Physics
  4. Halliday, Resnick, Walker - Fundamentals of Physics, 10th Edition
  5. Wikipedia: Transformer (article title)
  6. AQA A-Level Physics — Electromagnetic Induction