What is the transformer turns ratio formula?

The ideal transformer ties three ratios together: Np/Ns = Vp/Vs = Is/Ip. Np is the primary turns, Ns the secondary. So the turns ratio equals the voltage ratio. Example: a 100:10 transformer has a turns ratio of 10, and 120 V on the primary becomes 120 ÷ 10 = 12 V on the secondary. Type the four numbers and the tool applies that identity for you.

How do I tell step-up from step-down?

Compare the windings. If the primary has more turns than the secondary (Np greater than Ns), the secondary voltage is lower — that is a step-down transformer, like a 220 V to 12 V phone adapter. If the secondary has more turns (Ns greater than Np), the voltage rises — a step-up, like a 12 V to 230 V inverter. Equal turns give a 1:1 isolation transformer that passes voltage through unchanged.

Why does the current go up when the voltage goes down?

An ideal transformer conserves power: Vp·Ip = Vs·Is. If a 100:10 step-down cuts 120 V to 12 V (a factor of 10 lower), then 1 A on the primary becomes 10 A on the secondary (a factor of 10 higher). Current is inverse to voltage, which is why a low-voltage welding transformer can push hundreds of amps from a modest wall-current draw.

How is the impedance transform ratio calculated?

Impedance scales as the square of the turns ratio: Zp/Zs = (Np/Ns)². So a 10:1 turns ratio gives a 100:1 impedance ratio. This is how a tube amplifier's output transformer matches an 8-ohm speaker to a several-thousand-ohm plate load, and how RF baluns match antennas. The tool squares your turns ratio automatically and shows it as Zp:Zs.

How do I work out a 220 V to 12 V transformer?

Set the turns ratio to 220:12 (about 18.33:1). Put 220 V as the primary voltage and the tool shows 12 V on the secondary. Add the primary current, say 0.5 A, and it returns the secondary current of about 9.17 A from power conservation. You can also enter the actual winding counts if you know them — any Np and Ns that share the 18.33 ratio give the same voltages.

Does this match a real transformer exactly?

It uses the ideal model: no copper loss, no core loss, perfect magnetic coupling. Real transformers run a few percent below these figures because of winding resistance and leakage flux, and regulation droops under load. Use these numbers for design and sanity checks; for a finished build, measure the loaded secondary voltage and expect it a touch lower than the ideal answer.

Size a step-down transformer for a low-voltage supply

You need 12 V DC from a 220 V mains rail. Set the turns ratio to 220:12, drop in the mains voltage, and read 12 V on the secondary before you order an iron. Add the expected primary current and the tool tells you the secondary current from power conservation, so you can check the secondary winding gauge handles the amps it will carry.

Match an audio output transformer to a speaker

A tube amp's plate wants several thousand ohms but the speaker is 8 ohms. Because impedance scales as the turns ratio squared, you work backward: enter trial Np and Ns, read the Zp:Zs ratio, and tune the windings until the reflected load lands on the plate impedance the tube datasheet asks for. No square roots in your head.

Check an inverter or boost transformer design

Building a 12 V to 230 V inverter stage? Enter a 12:230 winding, confirm the step-up verdict, and watch the secondary current fall as the voltage climbs. The power figure stays flat, which is your reminder that a 100 W load at 230 V still pulls over 8 A from the 12 V battery side.

Solve transformer homework and lab problems

A circuits course question gives Np, Ns and a primary voltage and asks for the secondary voltage and current. Punch the numbers in, get the answer plus the formula it used, and copy a shareable link into your lab notebook so the worked example reopens exactly as you left it for the write-up.

Transformer Turns Ratio Calculator — Np/Ns, Vs, Is and Impedance

Np/Ns = Vp/Vs = Is/Ip — turns ratio, secondary voltage, current and impedance transform, step-up vs step-down — browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Enter the primary and secondary turns (Np, Ns), then a primary voltage and current. The tool solves the turns ratio, secondary voltage, secondary current and the impedance-transform ratio.

Common transformers

WindingsPrimary turns (Np)Secondary turns (Ns)

Primary sidePrimary voltage Vp (V)Primary current Ip (A)

Result

Step-down (Vs < Vp)

Turns ratio Np : Ns

100 : 10

Secondary voltage Vs

12 V

Secondary current Is

10 A

Impedance ratio Zp : Zs

100 : 1

Power (ideal, conserved): 120 W

Ideal model: no copper / core loss, perfect coupling. Real transformers run a few percent below these figures.

What this tool does

Free transformer turns ratio calculator for power supplies, audio matching, lab benches and electronics homework. Enter the primary and secondary turns (Np, Ns) plus a primary voltage and current, and the tool returns the turns ratio, the secondary voltage, the secondary current and the impedance-transform ratio in one shot. It works off the ideal transformer identity Np/Ns = Vp/Vs = Is/Ip, so a 100:10 winding driven at 120 V gives 12 V on the secondary, and because power is conserved (Vp·Ip = Vs·Is) the current rises by the same factor the voltage drops. The tool also flags whether the design is step-up, step-down or 1:1 isolation, and squares the turns ratio to give the impedance ratio used for output-transformer and antenna matching. Everything runs as plain JavaScript in your browser with one-click copy and a shareable URL that reproduces the exact transformer. 100% client-side, nothing uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Developer; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Transformer Turns Ratio Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Size a step-down transformer for a low-voltage supply
You need 12 V DC from a 220 V mains rail. Set the turns ratio to 220:12, drop in the mains voltage, and read 12 V on the secondary before you order an iron. Add the expected primary current and the tool tells you the secondary current from power conservation, so you can check the secondary winding gauge handles the amps it will carry.
Match an audio output transformer to a speaker
A tube amp's plate wants several thousand ohms but the speaker is 8 ohms. Because impedance scales as the turns ratio squared, you work backward: enter trial Np and Ns, read the Zp:Zs ratio, and tune the windings until the reflected load lands on the plate impedance the tube datasheet asks for. No square roots in your head.
Check an inverter or boost transformer design
Building a 12 V to 230 V inverter stage? Enter a 12:230 winding, confirm the step-up verdict, and watch the secondary current fall as the voltage climbs. The power figure stays flat, which is your reminder that a 100 W load at 230 V still pulls over 8 A from the 12 V battery side.
Solve transformer homework and lab problems
A circuits course question gives Np, Ns and a primary voltage and asks for the secondary voltage and current. Punch the numbers in, get the answer plus the formula it used, and copy a shareable link into your lab notebook so the worked example reopens exactly as you left it for the write-up.

Common pitfalls

Reading the turns ratio backward. Np/Ns is the primary over secondary ratio, so a 100:10 transformer has ratio 10 and steps DOWN to one-tenth the voltage. Flipping it makes a step-down look like a step-up. The tool labels the verdict so you can catch a swapped Np and Ns immediately.
Forgetting that current moves opposite to voltage. A step-down cuts voltage but multiplies current by the same factor. Sizing the secondary wire for the primary current undersizes it, because a 100:10 transformer carrying 1 A in carries 10 A out, and that winding must handle the larger number.
Using the ideal answer as the real loaded voltage. The model assumes zero loss and perfect coupling. A real secondary droops a few percent under load from winding resistance and leakage, so treat the tool's voltage as an upper bound and measure the built unit before committing to a regulator design.

Privacy

Every calculation — the turns ratio, the secondary voltage and current, the impedance transform and the power figure — is plain JavaScript that runs in your browser tab. No winding count, voltage or current ever leaves the page, and there is no logging of what you entered. The one caveat: the shareable URL encodes Np, Ns, Vp and Ip in the query string, so a share link pasted into chat records those numbers in the recipient server's access log. For anything sensitive, use the copy button and paste the text rather than sharing the URL.

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Transformer Turns Ratio Calculator — Np/Ns, Vs, Is and Impedance

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Transformer Turns Ratio Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Size a step-down transformer for a low-voltage supply

Match an audio output transformer to a speaker

Check an inverter or boost transformer design

Solve transformer homework and lab problems

Common pitfalls

Privacy

FAQ

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