Transformer Calculator (Turns Ratio & Power)

Transformer Guide

What should I know about Transformer Equations?

Voltage ratio equals turns ratio: Vp/Vs = Np/Ns. For an ideal transformer (100% efficiency): power in = power out. Vp × Ip = Vs × Is. Therefore: Ip/Is = Ns/Np. Voltage and current scale inversely with turns ratio — stepping up voltage steps down current by the same factor. Example: UK mains 230V to 12V. Ratio = 230/12 = 19.17:1. If primary current = 0.1A and efficiency 100%: secondary current = 0.1 × (230/12) = 1.92A. Secondary power = 12 × 1.92 = 23W = primary power.

What do I need to know about Step-Up and Step-Down?

Step-down transformer: Ns < Np — reduces voltage, increases current. Used in phone chargers, laptop adapters, doorbell transformers, welding equipment. Step-up transformer: Ns > Np — increases voltage, reduces current. Used in power transmission. National Grid transmits at 275-400kV — stepping up from power station output (~25kV) reduces current by 16× and therefore reduces power loss (P_loss = I²R) by 256× in the transmission lines. The electricity is then stepped back down through a series of substations closer to homes and businesses, reducing the voltage in stages until it reaches the safe level used inside a house.

What should I know about Transformer Losses?

Real transformers are typically 95-99% efficient. Losses: copper losses (I²R in the windings) — reduce by using thick copper wire. Core losses: eddy current losses (using laminated cores reduces these) and hysteresis losses (energy lost magnetising and demagnetising the core each cycle). Ideal transformer assumption: assumes no flux leakage and perfect coupling between primary and secondary coils. Efficiency = (output power / input power) × 100. A 95% efficient transformer delivering 100W output draws about 105W from the supply, with the remaining 5W lost mostly as heat in the windings and core.

What should I know about Applications?

Power supplies: every mains-powered device with a 'brick' adapter contains a transformer (often a high-frequency switching transformer). Isolation transformers: 1:1 ratio — no voltage change but electrically isolates the secondary circuit from the primary (safety in medical equipment and lab work). Current transformers: sense high currents in power lines for metering and protection. Audio transformers: impedance matching between amplifier and speaker. The turns ratio affects impedance as Z ∝ (N)

What's the key thing to understand about Why Transformers Only Work with AC?

Transformers rely entirely on electromagnetic induction, governed by Faraday's Law, which states that a voltage is induced in a coil only when the magnetic flux passing through it is changing — a constant, unchanging magnetic field induces no voltage at all, no matter how strong it is. An alternating current (AC) continuously reverses direction, which means the magnetic field it creates in the transformer's primary coil is also constantly changing, continuously inducing a corresponding alternating voltage in the secondary coil. A direct current (DC), by contrast, produces a steady, unchanging magnetic field once established, so after the brief instant when the DC is first switched on (when the field is indeed changing from zero to its steady value, briefly inducing a short voltage pulse), no further voltage is induced in the secondary coil at all. This is the fundamental physical reason transformers are a workhorse of AC power grids worldwide but cannot step up or down a steady DC voltage — DC-to-DC voltage conversion instead requires entirely different circuitry, such as switching converters, that artificially create a rapidly changing signal specifically so induction can take place.

What should I know about Ideal Power Conservation in Transformers?

An ideal transformer (one with no internal losses) conserves power exactly between its primary and secondary sides: power in equals power out, so Vp × Ip = Vs × Is, where V and I are voltage and current on the primary (p) and secondary (s) sides. Combined with the voltage-turns ratio, Vp/Vs = Np/Ns, this leads directly to an important consequence: the current ratio is the exact inverse of the turns ratio, Ip/Is = Ns/Np. In practical terms, this means a step-up transformer that increases voltage (more secondary turns than primary) must simultaneously decrease current by the same factor on the secondary side, and a step-down transformer that decreases voltage must simultaneously increase current by the same factor. For example, an ideal transformer stepping 120V up to 1,200V (a 10:1 step-up) would see secondary current at only 1/10th of the primary current for the same power level. This trade-off between voltage and current, with power held constant, is exactly why high-voltage, low-current transmission lines are used to move electrical power over long distances with reduced resistive losses, before transformers step the voltage back down for safer local distribution and use.

What should I know about a Worked Turns-Ratio Example?

A transformer with 1,000 primary turns and 100 secondary turns has a turns ratio of 10:1, so Np/Ns = Vp/Vs means a 230 V primary supply produces a 23 V secondary output. Because an ideal transformer conserves power, the current relationship runs the opposite way: Is/Ip = Np/Ns, so the secondary current is ten times the primary current (less voltage, proportionally more current) — exactly the trade-off that makes transformers so useful for converting high-voltage, low-current transmission power into the lower-voltage, higher-current form needed by household appliances.

Common Voltage Conversions and Their Turns Ratios

Worked Example: Transformer Efficiency and Losses

A transformer draws 230V at 2A on the primary (460 VA input, taking power factor ≈ 1 for simplicity, so 460W input) and delivers 400W to a 12V secondary load (33.3A output). Efficiency = Pout/Pin = 400/460 ≈ 86.96%, roughly 87%. The 60W difference is lost as heat, split between copper losses (resistive I²R heating in the windings, which rise with the square of load current) and core losses (magnetic hysteresis and eddy currents in the iron, which stay roughly constant regardless of load).

Why Transformer Losses Aren't Constant: Copper vs Core

Because copper losses scale with current squared while core losses stay almost fixed, a transformer's efficiency isn't flat across its load range — it's lowest at very light load (core losses dominate a tiny output) and also drops off at very heavy load (copper losses grow faster than output), with a peak efficiency point somewhere in between, typically around 50-80% of rated load for well-designed transformers. This is why manufacturers quote efficiency "at rated load" rather than as a single constant figure, and why running a transformer permanently at a small fraction of its rating (common when someone fits an oversized transformer "to be safe") can actually waste more energy proportionally than running one close to its design load.

Why Transformers Are Rated in kVA, Not kW

Transformer nameplates are usually rated in kVA (apparent power) rather than kW (real power), because the windings and core have to carry the full current regardless of the load's power factor, even though a poor power factor means less of that current is doing useful work. A transformer rated at 100kVA supplying a load with a power factor of 0.8 can only deliver 100 × 0.8 = 80kW of real power before it's fully loaded — which is why sizing a transformer purely from a load's kW figure, without checking its power factor, can lead to under-sizing.

Worked Example: Current and Power Through a Step-Down Transformer

A step-down transformer converts 240V mains to 12V for a low-voltage device, with a primary winding of 2000 turns. The turns ratio relationship N_p/N_s = V_p/V_s gives N_s = N_p × (V_s/V_p) = 2000 × (12/240) = 2000 × 0.05 = 100 turns on the secondary. If the secondary delivers 3A to the load, the secondary power is P_s = V_s × I_s = 12 × 3 = 36W. Assuming an ideal (lossless) transformer, primary power equals secondary power, so the primary current is I_p = P_s / V_p = 36 / 240 = 0.15A. Notice the inverse relationship: the voltage dropped by a factor of 20 (240 to 12) while the current increased by a factor of 20 (0.15A to 3A) -- transformers trade voltage for current, not power, which stays constant in the ideal case and only shrinks slightly once real-world copper and core losses are included.

Why Power Grids Transmit at High Voltage

Electrical transmission lines carry power at very high voltages (often 100 kV to over 500 kV) specifically to minimize resistive losses over long distances, and transformers are what make this possible at both ends of the line. For a fixed amount of power delivered, resistive loss in the transmission cable is P_loss = I^2 × R, so halving the current (by doubling the voltage, since P = VI) cuts resistive losses to one quarter. This is why power plants use step-up transformers to raise generated voltage to tens or hundreds of kilovolts for transmission, and substations use step-down transformers at multiple stages to bring voltage back down -- first to tens of kilovolts for regional distribution, then to the few hundred volts used in homes and businesses. Without transformers to step voltage up for transmission and back down for safe end use, long-distance electricity distribution as it exists today would be far too lossy and dangerous to be practical.