Convert Square Millimeter to Barn
Convert square millimeters to barns instantly. 1 square millimeter = 1e+22 barn — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Barn to Square Millimeter converter for the reverse conversion.
Units explained
Square Millimeter
A square millimeter is a metric unit of area equal to 10⁻⁶ m² (1 mm × 1 mm). It is widely used in engineering, electronics, and small-scale technical work.
Derived by squaring the millimeter, defined as 1/1000 of a meter. The milli- prefix comes from the Latin 'mille' (thousand).
Square millimeters express PCB trace cross-sections, the area of small mechanical features in CAD drawings, biological sample sizes, and material thicknesses.
Millimeter has been part of the metric system since 1795.
Barn
A barn is a scientific unit of area equal to exactly 10⁻²⁸ m² (100 fm²). It is used in nuclear and particle physics to express interaction cross-sections.
Named in 1942 at Purdue University by physicists working on the Manhattan Project. The name comes from the phrase 'big as a barn' — uranium nuclei have cross-sections this large, which physicists initially considered surprisingly large for nuclear targets.
Barns and their submultiples (millibarn, microbarn, nanobarn, picobarn, femtobarn) are the standard units for cross-section measurements in nuclear physics, high-energy physics, and accelerator experiments. The Higgs boson production cross-section at the LHC is in the picobarn range.
Named in 1942 during the Manhattan Project; adopted internationally in particle physics.
Square Millimeter to Barn conversion formula
The relationship between square millimeters and barns:
To convert square millimeters to barns, multiply the value in square millimeters by 1e+22. To reverse, multiply barns by 1e-22.
How to use this converter
Type a value into the calculator. The result in barns updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Barn to Square Millimeter converter for the reverse direction.
Step-by-step: convert square millimeters to barns
- Write down the value in square millimeters (mm²).
- Multiply that value by the factor 1e+22.
- The product is the equivalent value in barns (b).
- To reverse, multiply the barn value by 1e-22.
Worked examples
Example 1 — Convert 1 mm² to b:
1 × 1e+22 = 1e+22 b
Example 2 — Convert 100 mm² to b:
100 × 1e+22 = 1e+24 b
Real-world example — Infrared to visible-spectrum mapping
A 10-square millimeter thermal infrared wavelength corresponds to a much larger number in barns, the unit favoured for ultraviolet and visible-light specifications.
10 mm² × 1e+22 = 1e+23 b
Real-world example — Mid-micron to nanometer
3 square millimeters equals 3,000 barns — useful when relating mid-infrared wavelengths (typically quoted in microns) to nanometer-scale visible-light wavelength tables.
3 mm² × 1e+22 = 3e+22 b
Real-world example — From microns to sub-micron features
One square millimeter equals one thousand barns — the conversion semiconductor designers do constantly when comparing mask feature dimensions to actual transistor gate lengths.
1 mm² × 1e+22 = 1e+22 b
Square Millimeter to Barn conversion table
Standard reference values for converting square millimeters to barns:
| Square Millimeter [mm²] | Barn [b] |
|---|---|
| 0.01 | 1e+20 |
| 0.1 | 1e+21 |
| 1 | 1e+22 |
| 2 | 2e+22 |
| 3 | 3e+22 |
| 4 | 4e+22 |
| 5 | 5e+22 |
| 10 | 1e+23 |
| 20 | 2e+23 |
| 30 | 3e+23 |
| 40 | 4e+23 |
| 50 | 5e+23 |
| 100 | 1e+24 |
| 500 | 5e+24 |
| 1000 | 1e+25 |
Frequently asked questions
How many barns is 1 square millimeter?
How do I convert square millimeters to barns?
How do I convert barns back to square millimeters?
How many barns is 100 square millimeters?
Popular area unit conversions
Convert Square Millimeter to other area units
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Metric / SI (15 units)
Imperial / US Customary (15 units)
US Survey (5 units)
Indian Subcontinent (16 units)
Other Regional (10 units)
Scientific / Physics (5 units)
Sources & references
Conversion factor (1 mm² = 1e+22 b) verified against the following authoritative sources:
- BIPM — The International System of Units (SI Brochure 9th ed.)
Official BIPM publication defining the seven SI base units (including the meter) and the rules for their use. The global authority on units of measurement.
- NIST — Guide to the SI
US National Institute of Standards and Technology reference covering the SI base and derived units with definitions and usage rules for US technical practice.
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Detailed NIST guide covering exact conversion factors between SI and US customary units along with formatting and rounding conventions.
- NIST — Refinement of values for the yard and pound (Federal Register 1959)
The treaty (signed by US
- International Astronomical Union — System of Astronomical Constants
The IAU defines astronomical units including the AU (149597870700 m exactly) light-year and parsec used in astronomy and astrophysics.