Convert Barn to Square Millimeter
Convert barns to square millimeters instantly. 1 barn = 1e-22 square millimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Square Millimeter to Barn converter for the reverse conversion.
Units explained
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
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 to Square Millimeter conversion formula
The relationship between barns and square millimeters:
To convert barns to square millimeters, multiply the value in barns by 1e-22. To reverse, multiply square millimeters by 1e+22.
How to use this converter
Type a value into the calculator. The result in square millimeters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Square Millimeter to Barn converter for the reverse direction.
Step-by-step: convert barns to square millimeters
- Write down the value in barns (b).
- Multiply that value by the factor 1e-22.
- The product is the equivalent value in square millimeters (mm²).
- To reverse, multiply the square millimeter value by 1e+22.
Worked examples
Example 1 — Convert 1 b to mm²:
1 × 1e-22 = 1e-22 mm²
Example 2 — Convert 100 b to mm²:
100 × 1e-22 = 1e-20 mm²
Real-world example — Spanning sub-micron to micron scale
Crossing from barns to square millimeters is the everyday workflow of microscopy and semiconductor engineering — a measurement of 1000 barns translates to a much more compact value in square millimeters that fits the scale of biological cells and process nodes.
1000 b × 1e-22 = 1e-19 mm²
Real-world example — Sub-visible-light wavelength
500 barns (the green-yellow visible band) equals 0.5 square millimeters — the canonical conversion in optics between wavelength specifications and micron-scale lens-coating thicknesses.
500 b × 1e-22 = 5e-20 mm²
Barn to Square Millimeter conversion table
Standard reference values for converting barns to square millimeters:
| Barn [b] | Square Millimeter [mm²] |
|---|---|
| 0.01 | 1e-24 |
| 0.1 | 1e-23 |
| 1 | 1e-22 |
| 2 | 2e-22 |
| 3 | 3e-22 |
| 4 | 4e-22 |
| 5 | 5e-22 |
| 10 | 1e-21 |
| 20 | 2e-21 |
| 30 | 3e-21 |
| 40 | 4e-21 |
| 50 | 5e-21 |
| 100 | 1e-20 |
| 500 | 5e-20 |
| 1000 | 1e-19 |
Frequently asked questions
How many square millimeters is 1 barn?
How do I convert barns to square millimeters?
How do I convert square millimeters back to barns?
How many square millimeters is 100 barns?
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Sources & references
Conversion factor (1 b = 1e-22 mm²) 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 Hydrographic Organization — Resolution on the Nautical Mile
International authority that standardised the nautical mile at exactly 1852 m in 1929 — the value adopted worldwide for sea and air navigation.