Ohms to Henries Converter
A coil with 100 ohms of reactance at 50 hertz has an inductance of about 0.318 henry.
Quick answer: Divide the reactance by 2 times pi times the frequency. For example, 100 ohms at 50 Hz is 0.3183 H, 377 ohms at 60 Hz is 1 H and 1,000 ohms at 1,000 Hz is 0.1592 H.
The ohms to henries formula
Inductance in henries equals reactance divided by 2 times pi times frequency.
The reactance must be inductive reactance in ohms, and the frequency must be in hertz.
Take 100 ohms at 50 Hz. 100 ÷ (2 × π × 50) gives 0.3183 H.
Take 377 ohms at 60 Hz. 377 ÷ (2 × π × 60) gives 1 H.
Reactance, not plain resistance
Inductive reactance is the opposition an inductor gives to alternating current. It equals 2 times pi times frequency times inductance and is measured in ohms (Wikipedia: Electrical reactance).
Because it rises with frequency, you must know the frequency to turn ohms into henries.
How to convert ohms to henries step by step
- Read the inductive reactance in ohms and the frequency in hertz.
- Multiply the frequency by 2 times pi, which is about 6.2832.
- Divide the reactance by that number.
- Read the answer in henries, or multiply by 1,000 for millihenries.
Example 1: 100 ohms at 50 Hz
- Start with 100 ohms at 50 Hz.
- 100 ÷ (2 × π × 50) = 0.3183.
- The inductance is 0.3183 H.
100 ohms at 50 Hz = 0.3183 H
Example 2: 377 ohms at 60 Hz
- Start with 377 ohms at 60 Hz.
- 377 ÷ (2 × π × 60) = 1.
- The inductance is 1 H.
377 ohms at 60 Hz = 1 H
Example 3: 1,000 ohms at 1,000 Hz
- Start with 1,000 ohms at 1,000 Hz.
- 1,000 ÷ (2 × π × 1,000) = 0.1592.
- The inductance is 0.1592 H.
1,000 ohms at 1,000 Hz = 0.1592 H
The three examples below use common sizes.
Each one shows the sum in full.
ohms to henries conversion table
| Reactance and frequency | Inductance (H) | Inductance (mH) |
|---|---|---|
| 10 ohms at 50 Hz | 0.0318 H | 31.831 mH |
| 25 ohms at 50 Hz | 0.0796 H | 79.577 mH |
| 50 ohms at 50 Hz | 0.1592 H | 159.15 mH |
| 100 ohms at 50 Hz | 0.3183 H | 318.31 mH |
| 100 ohms at 60 Hz | 0.2653 H | 265.26 mH |
| 200 ohms at 60 Hz | 0.5305 H | 530.52 mH |
| 377 ohms at 60 Hz | 1 H | 1,000.02 mH |
| 500 ohms at 100 Hz | 0.7958 H | 795.77 mH |
| 1,000 ohms at 100 Hz | 1.592 H | 1,591.55 mH |
| 1,000 ohms at 1,000 Hz | 0.1592 H | 159.15 mH |
| 5,000 ohms at 1,000 Hz | 0.7958 H | 795.77 mH |
| 10,000 ohms at 10,000 Hz | 0.1592 H | 159.15 mH |
The highlighted row is the default of the calculator. The last column gives mH.
A quick mental shortcut for ohms to henries
Divide the reactance by 6.28, then divide by the frequency. For 100 ohms at 50 Hz that is 100 / 6.28 / 50, which is about 0.32 H.
Raise the frequency tenfold and the same reactance means an inductance ten times smaller.
Why a plain resistance meter fails
A resistance meter uses direct current, so it only reads the wire resistance of the coil. That tells you nothing about its inductance.
You need an AC measurement at a known frequency, or an inductance meter.
Mains frequency examples
At 60 Hz, a reactance of 377 ohms means an inductance of about 1 H, because 2 times pi times 60 is about 377.
At 50 Hz the same 1 H coil has a reactance of about 314 ohms.
Ideal inductor only
The formula treats the coil as an ideal inductor. Real coils also have wire resistance and some capacitance between turns.
Near the self-resonant frequency of a real coil, the formula stops being a good guide.
Quick conversion answers
| Conversion | Result |
|---|---|
| 100 ohms at 50 Hz | 0.3183 H |
| 377 ohms at 60 Hz | 1 H |
| 1,000 ohms at 1,000 Hz | 0.1592 H |
| 5,000 ohms at 1,000 Hz | 0.7958 H |
Where this conversion is used
Students turn a measured reactance into a coil value.
Technicians check a choke or a motor winding against its stated inductance.
Common mistakes to avoid
- Using the DC resistance. The formula needs reactance at one frequency.
- Forgetting the 2 times pi. Skipping it gives an answer 6.28 times too large.
- Using kHz as Hz. A frequency of 1 kHz is 1,000 Hz.
- Stating the answer in the wrong unit. The main result is in henries, not millihenries.
Related converters
More reactance and frequency pairs
20 ohms at 50 Hz is 0.06366 H. 60 ohms at 60 Hz is 0.1592 H. 150 ohms at 50 Hz is 0.4775 H.
250 ohms at 60 Hz is 0.6631 H. 400 ohms at 400 Hz is 0.1592 H. 750 ohms at 1,000 Hz is 0.1194 H.
1,200 ohms at 500 Hz is 0.382 H. 2,000 ohms at 1,000 Hz is 0.3183 H. 8,000 ohms at 5,000 Hz is 0.2546 H.
Doubling the first number
40 ohms at 50 Hz is 0.1273 H. 120 ohms at 60 Hz is 0.3183 H. 300 ohms at 50 Hz is 0.9549 H.
500 ohms at 60 Hz is 1.326 H. 800 ohms at 400 Hz is 0.3183 H. 1,500 ohms at 1,000 Hz is 0.2387 H.
2,400 ohms at 500 Hz is 0.7639 H. 4,000 ohms at 1,000 Hz is 0.6366 H. 16,000 ohms at 5,000 Hz is 0.5093 H.
The same reactance at different frequencies
100 ohms at 50 Hz is 0.3183 H. 100 ohms at 60 Hz is 0.2653 H. 100 ohms at 400 Hz is 0.03979 H.
100 ohms at 1,000 Hz is 0.01592 H.
Frequently asked questions
How do I convert ohms to henries?
Divide the inductive reactance by 2 times pi times the frequency in hertz.
How many henries is 100 ohms at 50 Hz?
About 0.3183 H, which is 318.3 mH.
Can I convert plain resistance to henries?
No. Resistance does not set inductance. You need the reactance at a known frequency.
What is the 2 pi for?
It turns a frequency in hertz into an angular frequency in radians per second.
How do I get millihenries?
Multiply the henries by 1,000.
Does the answer change with frequency?
The coil does not change. The reactance you measure does, so give both numbers.
Sources
- Wikipedia: Electrical reactance (en.wikipedia.org)
