Transformer calculations: worked examples
By Engr. Mehmood Kakar · Updated
Quick answer
Use Vp ÷ Vs = np ÷ ns for turns and voltages, and VpIp = VsIs for currents. Keep primary on top on both sides. A step-up transformer has more secondary turns, so the p.d. goes up and the current goes down by the same factor.
The two transformer equations
- Vp ÷ Vs = np ÷ ns: links the potential differences to the numbers of turns
- Vp × Ip = Vs × Is: power in equals power out, for a 100% efficient transformer
Both are on the equation sheet. Label every number p or s before you substitute; mixing up the coils is the most common error.
Step-down: finding the output p.d.
A transformer has 4600 turns on the primary coil and 240 on the secondary. It is connected to 230 V mains. Calculate the output p.d. (3 marks)
- Vs = Vp × ns ÷ np
- Vs = 230 × 240 ÷ 4600
- Vs = 12 V
Step-up transformers
A transformer has 100 primary turns and 2500 secondary turns. The input is 400 V. Calculate the output p.d. (2 marks)
- Vs = 400 × 2500 ÷ 100
- Vs = 10,000 V
The secondary has 25 times as many turns, so the p.d. is 25 times bigger. That ratio check is quick and catches most slips.
Finding the number of turns
A transformer steps 25 kV up to 400 kV. The primary coil has 500 turns. How many turns does the secondary have? (3 marks)
- ns = np × Vs ÷ Vp
- ns = 500 × 400 ÷ 25 (both p.d.s in kV, so no conversion needed)
- ns = 8000 turns
Finding the current
A transformer draws 0.20 A from 230 V mains and gives an output of 11.5 V. Assuming it is 100% efficient, calculate the output current. (3 marks)
- Vp × Ip = Vs × Is
- Is = 230 × 0.20 ÷ 11.5 = 46 ÷ 11.5
- Is = 4.0 A
Two-step questions
A transformer has 2000 primary turns and 100 secondary turns and is connected to 230 V. The output current is 3.0 A. Calculate the input current. (5 marks)
- Step 1, output p.d.: Vs = 230 × 100 ÷ 2000 = 11.5 V
- Step 2, power: VpIp = VsIs
- Ip = 11.5 × 3.0 ÷ 230
- Ip = 0.15 A
Why the National Grid uses transformers
Power stations use step-up transformers to raise the p.d. to hundreds of thousands of volts. For the same power, a higher p.d. means a smaller current. The energy wasted heating the cables depends on the current squared (P = I²R), so a smaller current wastes far less energy. Step-down transformers near homes then reduce the p.d. to a safe 230 V.
Practice
1. A transformer has 920 primary turns and 40 secondary turns. The input is 230 V. Calculate the output p.d.
Vs = 230 × 40 ÷ 920 → Vs = 10 V
2. A transformer steps 11 kV up to 275 kV. The primary has 400 turns. How many turns are on the secondary?
ns = 400 × 275 ÷ 11 → ns = 10,000 turns
3. A transformer takes 200 A at 25 kV and outputs 400 kV. Assuming 100% efficiency, calculate the output current.
Is = 25 × 200 ÷ 400 (p.d.s both in kV) → Is = 12.5 A
Frequently asked questions
How do you work out the output voltage of a transformer?
Use Vs = Vp × ns ÷ np. Multiply the input p.d. by the ratio of secondary turns to primary turns.
How can you tell if a transformer is step-up or step-down?
Compare the turns. More turns on the secondary coil means step-up (Vs > Vp). Fewer turns on the secondary means step-down (Vs < Vp).
What happens to the current in a step-up transformer?
It goes down. If the transformer is 100% efficient, power in equals power out, so stepping the p.d. up by a factor steps the current down by the same factor.
Are transformer calculations Higher tier?
Yes. In AQA, transformers are in GCSE Physics (separate science) only, and the calculations are Higher tier.
Written by Engr. Mehmood Kakar
Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)
Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.