Length · Unit Converter

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.

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

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.

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.

Barn to Square Millimeter conversion formula

The relationship between barns and square millimeters:

1 b = 1e-22 mm²
1 mm² = 1e+22 b

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

  1. Write down the value in barns (b).
  2. Multiply that value by the factor 1e-22.
  3. The product is the equivalent value in square millimeters (mm²).
  4. 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]
0.011e-24
0.11e-23
11e-22
22e-22
33e-22
44e-22
55e-22
101e-21
202e-21
303e-21
404e-21
505e-21
1001e-20
5005e-20
10001e-19

Frequently asked questions

How many square millimeters is 1 barn?
1 barn equals 1e-22 square millimeter.
How do I convert barns to square millimeters?
Multiply the value in barns by 1e-22 to get square millimeters.
How do I convert square millimeters back to barns?
Multiply the value in square millimeters by 1e+22, or use the Square Millimeter to Barn converter.
How many square millimeters is 100 barns?
100 barns equals 1e-20 square millimeters, because 100 × 1e-22 = 1e-20.

Convert Barn to other area units

Show all Barn conversions

Sources & references

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

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