Transformer Calculator
Calculate transformer voltage, turns ratio, or number of turns using the transformer equation Vp/Vs = Np/Ns. Determine secondary voltage, primary voltage, or winding turns for step-up and step-down transformers. See also our Ohm's Law Calculator and Voltage Drop Calculator.
How Transformers Work
A transformer transfers electrical energy between two circuits through electromagnetic induction. It consists of two or more coils (windings) wound around a common magnetic core. When alternating current flows through the primary winding, it creates a changing magnetic flux in the core, which induces a voltage in the secondary winding. The voltage ratio equals the turns ratio — this fundamental relationship allows transformers to step voltage up or down.
Transformers are essential to the electrical power grid, enabling efficient long-distance power transmission at high voltage (reducing I²R losses) and safe distribution at lower voltages for end users. They also provide electrical isolation between circuits, which is critical for safety and noise reduction in electronic equipment.
Transformer Formulas
Voltage Ratio (Turns Ratio):
Vp/Vs = Np/Ns
Vs = Vp × (Ns/Np)
Current Ratio (inverse of voltage ratio):
Ip/Is = Ns/Np
Is = Ip × (Np/Ns)
Power (ideal transformer):
Pp = Ps (input power = output power)
Vp × Ip = Vs × Is
Impedance Transformation:
Zp = Zs × (Np/Ns)²
Efficiency:
η = Pout/Pin × 100%
Losses = Core losses + Copper losses
Example Calculation
A transformer with 1000 primary turns and 100 secondary turns, connected to 120V:
Turns ratio: a = Np/Ns = 1000/100 = 10:1 (step-down)
Secondary voltage: Vs = 120 × (100/1000) = 12V
If secondary load draws 2A:
Secondary power: Ps = 12V × 2A = 24W
Primary current: Ip = Is × (Ns/Np) = 2 × (100/1000) = 0.2A
Primary power: Pp = 120V × 0.2A = 24W ✓ (ideal)
Impedance transformation:
If secondary load = 6Ω:
Reflected to primary: Zp = 6 × (1000/100)² = 6 × 100 = 600Ω
With 95% efficiency:
Actual Pin = 24W / 0.95 = 25.3W
Losses = 25.3 - 24 = 1.3W (heat in core and windings)
Transformer Reference Table
| Vp (V) | Np | Ns | Vs (V) | Type |
|---|---|---|---|---|
| 120 | 1000 | 100 | 12 | Step-down |
| 120 | 1000 | 200 | 24 | Step-down |
| 120 | 500 | 500 | 120 | Isolation |
| 120 | 100 | 1000 | 1200 | Step-up |
| 240 | 1000 | 500 | 120 | Step-down |
| 240 | 2000 | 100 | 12 | Step-down |
| 240 | 1000 | 42 | 10 | Step-down |
| 480 | 2000 | 500 | 120 | Step-down |
| 120 | 500 | 2000 | 480 | Step-up |
| 12 | 100 | 1000 | 120 | Step-up |
| 120 | 1000 | 50 | 6 | Step-down |
| 240 | 1000 | 1000 | 240 | Isolation |
Frequently Asked Questions
What is a turns ratio?
The turns ratio (a = Np/Ns) is the ratio of primary to secondary winding turns. It directly determines the voltage transformation: a 10:1 ratio means the secondary voltage is 1/10 of the primary (step-down). A 1:10 ratio means the secondary is 10× the primary (step-up). The current ratio is the inverse of the turns ratio to conserve power.
Can a transformer work with DC?
No. Transformers require changing magnetic flux to induce voltage in the secondary. DC creates a constant flux that induces no voltage (except during transients). Applying DC to a transformer primary results in very high current (limited only by winding resistance) that will overheat and destroy the transformer. DC-DC conversion requires first converting DC to AC (using an inverter/oscillator), transforming, then rectifying back to DC.
What determines transformer efficiency?
Transformer losses come from two sources: copper losses (I²R heating in windings, proportional to load current squared) and core losses (hysteresis and eddy currents in the magnetic core, roughly constant regardless of load). Large power transformers achieve 95-99% efficiency. Small transformers (wall adapters) are typically 80-90% efficient. Efficiency is highest at the load level where copper losses equal core losses.
What is impedance matching with transformers?
Transformers can match source impedance to load impedance for maximum power transfer. The impedance transforms by the square of the turns ratio: Zp = Zs × (Np/Ns)². For example, matching an 8Ω speaker to a 600Ω amplifier output requires a = √(600/8) = 8.66:1 turns ratio. This is used in audio systems, RF circuits, and antenna matching.
What is the difference between step-up and step-down transformers?
A step-down transformer has more primary turns than secondary (Np > Ns), producing lower secondary voltage but higher secondary current. A step-up transformer has fewer primary turns (Np < Ns), producing higher secondary voltage but lower current. The same physical transformer can be used as either by swapping which winding is connected to the source.
Why do transformers hum?
The humming sound (at 120Hz for 60Hz power, or 100Hz for 50Hz) is caused by magnetostriction — the physical expansion and contraction of the core material as it magnetizes and demagnetizes each half cycle. Loose laminations amplify the vibration. Higher-quality transformers use tightly clamped, grain-oriented silicon steel cores to minimize hum. Overloaded or failing transformers may hum louder than normal.
Types of Transformers
Transformers come in many configurations for different applications. Power transformers handle high power at line frequency (50/60Hz) for distribution and industrial use. Isolation transformers provide galvanic isolation for safety without changing voltage (1:1 ratio). Autotransformers use a single tapped winding for compact voltage adjustment. Current transformers (CTs) measure high currents by stepping them down to safe levels. Pulse transformers handle fast transients in digital circuits and gate drivers. High-frequency transformers in switching power supplies operate at 50kHz-1MHz, enabling much smaller cores.
Practical Applications
- Power distribution: Step up to 765kV for transmission, step down to 120/240V for homes
- Phone chargers: Switch-mode transformers convert 120V AC to 5V DC efficiently
- Audio systems: Output transformers match tube amplifier impedance to speakers
- Welding: Step-down transformers provide high current at low voltage for arc welding
- Neon signs: Step-up transformers produce 2-15kV for gas discharge tubes
- Medical equipment: Isolation transformers protect patients from ground faults
Safety Considerations
Transformers connected to mains voltage present serious electrical hazards. The secondary of a step-up transformer can produce lethal voltages. Even step-down transformers can deliver dangerous currents at low voltage. Always de-energize transformers before working on them. Isolation transformers do NOT protect against shock from the secondary — they only prevent ground-fault current paths. Never exceed a transformer's VA rating, as overloading causes overheating and potential fire. Oil-filled transformers require special handling due to potential PCB contamination in older units.