Transformer Calculations

Transformers change voltage levels to match the needs of different equipment. Every commercial building has them — stepping 480V down to 208V/120V for receptacles and lighting. Understanding the turns ratio and current relationships lets you size transformers, calculate secondary current, and verify that overcurrent protection is correct.

The Turns Ratio

A transformer’s voltage ratio equals its turns ratio:

$\frac{V_p}{V_s} = \frac{N_p}{N_s}$

Where:

• $V_p$ = Primary voltage (input)
• $V_s$ = Secondary voltage (output)
• $N_p$ = Number of turns on the primary winding
• $N_s$ = Number of turns on the secondary winding

Step-down transformer: $V_p > V_s$ (reduces voltage, increases current) Step-up transformer: $V_p < V_s$ (increases voltage, reduces current)

The Current Relationship

Power in equals power out (ignoring losses), so current is inversely proportional to voltage:

$V_p \times I_p = V_s \times I_s$

$\frac{I_p}{I_s} = \frac{V_s}{V_p}$

When voltage goes down, current goes up by the same ratio — and vice versa. This is why low-voltage secondary circuits require larger conductors.

kVA Sizing

Transformers are rated in kilovolt-amperes (kVA), not watts, because they must handle the full apparent power regardless of power factor.

$\text{kVA} = \frac{V \times I}{1{,}000}$

Single-phase:

$I = \frac{\text{kVA} \times 1{,}000}{V}$

Three-phase:

$\text{kVA} = \frac{V \times I \times \sqrt{3}}{1{,}000} \qquad I = \frac{\text{kVA} \times 1{,}000}{V \times \sqrt{3}}$

Worked Examples

Example 1: 480V to 120V Step-Down

Scenario: A single-phase transformer steps 480V primary down to 120V secondary. The secondary feeds a 20A load. What is the turns ratio and primary current?

Turns ratio:

$\frac{V_p}{V_s} = \frac{480}{120} = \frac{4}{1}$

The turns ratio is 4:1 — for every 4 turns on the primary, there is 1 turn on the secondary.

Primary current:

$V_p \times I_p = V_s \times I_s$

$480 \times I_p = 120 \times 20$

$I_p = \frac{2{,}400}{480} = 5 \text{ A}$

Answer: The primary draws 5 amps. The 4:1 voltage reduction produces a 1:4 current increase from primary to secondary (5A primary, 20A secondary).

Example 2: Sizing a Transformer for a Lighting Panel

Scenario: A lighting panel has a calculated load of 18,000 VA at 208V single-phase. The building supply is 480V. What size transformer is needed, and what are the primary and secondary currents?

kVA sizing:

$\text{kVA} = \frac{18{,}000}{1{,}000} = 18 \text{ kVA}$

The next standard transformer size is 25 kVA (standard sizes: 3, 5, 7.5, 10, 15, 25, 37.5, 50, 75, 100 kVA).

Secondary current (at full 25 kVA rating):

$I_s = \frac{25{,}000}{208} = 120.2 \text{ A}$

Primary current (at full 25 kVA rating):

$I_p = \frac{25{,}000}{480} = 52.1 \text{ A}$

Answer: Use a 25 kVA transformer. Secondary current at full load is 120.2A; primary current is 52.1A.

Example 3: Verifying a Transformer is Not Overloaded

Scenario: A 15 kVA, 480V/120V single-phase transformer feeds several circuits. You measure 110A total on the secondary. Is the transformer overloaded?

Maximum secondary current at rated kVA:

$I_{s(\text{max})} = \frac{15{,}000}{120} = 125 \text{ A}$

Since 110A < 125A, the transformer is operating within its rating.

Current load as percentage:

$\%\text{Load} = \frac{110}{125} \times 100 = 88\%$

Answer: The transformer is at 88% of capacity — not overloaded, but approaching full load. Monitor for additional loads.

Reference Table: Standard Single-Phase Transformer Sizes

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Common Mistakes to Avoid

1. Confusing the voltage and current ratios. Voltage ratio equals the turns ratio. Current ratio is the inverse of the turns ratio. When voltage goes down, current goes up.
2. Sizing a transformer to the exact load. Always select the next standard size above the calculated load. A 22 kVA load requires a 25 kVA transformer, not a 15 kVA.
3. Forgetting to use VA, not watts, for transformer sizing. Transformers are rated in kVA because they must supply the full apparent power. A 10 kW load at 0.8 power factor requires $\frac{10{,}000}{0.8} = 12{,}500$ VA (12.5 kVA), not 10 kVA.
4. Assuming zero losses. Real transformers have 2-5% losses. For critical sizing, add a margin above the calculated kVA.

Key Takeaways

• The turns ratio determines the voltage ratio: $\frac{V_p}{V_s} = \frac{N_p}{N_s}$
• Current is inversely proportional to voltage: when voltage steps down, current steps up
• Transformers are sized in kVA, not watts — always select the next standard size above the calculated load
• Use $I = \frac{\text{kVA} \times 1{,}000}{V}$ to find the maximum current at any voltage
• The current relationship ($V_p \times I_p = V_s \times I_s$) lets you find primary current from secondary measurements and vice versa

Math for Electricians