Convert Radians to Milliradians
1 radian is 1,000 mrad. One radian is exactly 1000 milliradians.
One radian is 1000 milliradians. To convert radians to milliradians, multiply by 1000; to go the other way, divide by 1000 or multiply by 0.001. The factor is exact rather than rounded: it follows from NIST Special Publication 811. The angle subtending an arc equal to the radius.
Factor checked against the defining standard · How we check
- Radians × 1000
1 * 10001,000 mrad
1 radian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians (as entered) | 1 rad | — |
| degrees | 57.29577951 ° | × 57.2957795131 |
| gradians | 63.66197724 gon | × 63.6619772368 |
| arcminutes | 3,437.746771 ′ | × 3,437.74677078 |
| arcseconds | 206,264.8062 ″ | × 206,264.806247 |
| turns | 0.1591549431 turn | × 0.159154943092 |
| milliradians | 1,000 mrad | × 1,000 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert radians to milliradians? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 1000 — that is how many milliradians fit in one radian.
- 3.To go back the other way, divide by 1000, or multiply by 0.001.
Worked example: 25 radians to milliradians
- Formula
- rad × 1000 = mrad
- Arithmetic
- 25 × 1000 = 25,000 mrad
- Answer
- 25 rad = 25,000 mrad
The factor is exact, so this figure is exact too — only the display is rounded.
Radians to milliradians conversion table
| Radians | Milliradians |
|---|---|
| 1 rad | 1,000 mrad |
| 2 rad | 2,000 mrad |
| 3 rad | 3,000 mrad |
| 4 rad | 4,000 mrad |
| 5 rad | 5,000 mrad |
| 6 rad | 6,000 mrad |
| 7 rad | 7,000 mrad |
| 8 rad | 8,000 mrad |
| 9 rad | 9,000 mrad |
| 10 rad | 10,000 mrad |
| 12 rad | 12,000 mrad |
| 15 rad | 15,000 mrad |
| 20 rad | 20,000 mrad |
| 25 rad | 25,000 mrad |
| 50 rad | 50,000 mrad |
| 100 rad | 100,000 mrad |
| 200 rad | 200,000 mrad |
| 300 rad | 300,000 mrad |
| 500 rad | 500,000 mrad |
| 1000 rad | 1,000,000 mrad |
| 2000 rad | 2,000,000 mrad |
| 5000 rad | 5,000,000 mrad |
| 10000 rad | 10,000,000 mrad |
What is a radian?
The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
What is a milliradian?
A thousandth of a radian, and the unit rifle scopes adjust in: at 100 meters one milliradian moves the point of impact by 10 cm. The military "mil" is a different thing — 6,400 to a turn rather than the true 6,283.
How many milliradians are in a radian?
One radian is 1000 milliradians, exactly. Going the other way, one milliradian is 0.001 radians. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to a radian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Radians to milliradians. Rule Calculator. https://rulecalculators.com/convert/radian-to-milliradian
- MLA
- "Convert Radians to milliradians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-milliradian.
- Chicago
- Rule Calculator. "Convert Radians to milliradians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-milliradian.
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Questions people actually ask
- How many milliradians are in a radian?
- 1000. A thousandth of a radian, and the unit rifle scopes adjust in: at 100 meters one milliradian moves the point of impact by 10 cm. The military "mil" is a different thing — 6,400 to a turn rather than the true 6,283.
- How do I convert milliradians back to radians?
- Divide by 1000, or multiply by 0.001 — they are the same operation.
Other angle conversions
Milliradians to radians — the same conversion the other way.