Length · Unit Converter

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.

Written by Sunith Babu L, Ph.D., Lead Engineer Reviewed by Girish V Kulkarni Ph.D.
Length category 2 min read Published Last reviewed Updated

Units explained

Metric / SI

Square Millimeter

What is a 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.

Origin of the square millimeter

Derived by squaring the millimeter, defined as 1/1000 of a meter. The milli- prefix comes from the Latin 'mille' (thousand).

Where it is used

Square millimeters express PCB trace cross-sections, the area of small mechanical features in CAD drawings, biological sample sizes, and material thicknesses.

When and where it was developed

Millimeter has been part of the metric system since 1795.

Scientific / Physics

Barn

What is a 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.

Origin of the barn

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.

Where it is used

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.

When and where it was developed

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:

1 mm² = 1e+22 b
1 b = 1e-22 mm²

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

  1. Write down the value in square millimeters (mm²).
  2. Multiply that value by the factor 1e+22.
  3. The product is the equivalent value in barns (b).
  4. 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]
0.011e+20
0.11e+21
11e+22
22e+22
33e+22
44e+22
55e+22
101e+23
202e+23
303e+23
404e+23
505e+23
1001e+24
5005e+24
10001e+25

Frequently asked questions

How many barns is 1 square millimeter?
1 square millimeter equals 1e+22 barn.
How do I convert square millimeters to barns?
Multiply the value in square millimeters by 1e+22 to get barns.
How do I convert barns back to square millimeters?
Multiply the value in barns by 1e-22, or use the Barn to Square Millimeter converter.
How many barns is 100 square millimeters?
100 square millimeters equals 1e+24 barns, because 100 × 1e+22 = 1e+24.

Convert Square Millimeter to other area units

Show all Square Millimeter conversions
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)
Historical / Pre-metric European (6 units)

Sources & references

Conversion factor (1 mm² = 1e+22 b) verified against the following authoritative sources:

Results are provided for general reference. Verify critical measurements against an authoritative standard.