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Formula

In a general physics context, sectional density is defined as:

S D = M A {\displaystyle SD={\frac {M}{A}}} ²

• SD is the sectional density
• M is the mass of the projectile
• A is the cross-sectional area

The SI derived unit for sectional density is kilograms per square meter (kg/m2). The general formula with units then becomes:

S D kg / m 2 = m kg A m 2 {\displaystyle SD_{{\text{kg}}/{\text{m}}^{2}}={\frac {m_{\text{kg}}}{A_{{\text{m}}^{2}}}}}

where:

• SDkg/m2 is the sectional density in kilograms per square meters
• mkg is the weight of the object in kilograms
• Am2 is the cross sectional area of the object in meters

Units conversion table

Conversions between units for sectional density

	kg/m2	kg/cm2	g/mm2	lbm/in2
1 kg/m2 =	1	0.0001	0.001	0.001422334
1 kg/cm2 =	10000	1	10	14.223343307
1 g/mm2 =	1000	0.1	1	1.4223343307
1 lbm/in2 =	703.069579639	0.070306957	0.703069579	1

(Values in bold face are exact.)

• 1 g/mm2 equals exactly 1000 kg/m2.
• 1 kg/cm2 equals exactly 10000 kg/m2.
• With the pound and inch legally defined as 0.45359237 kg and 0.0254 m respectively, it follows that the (mass) pounds per square inch is approximately: 1 lbm/in2 = 0.45359237 kg/(0.0254 m × 0.0254 m) ≈ 703.06958 kg/m2

Use in ballistics

The sectional density of a projectile can be employed in two areas of ballistics. Within external ballistics, when the sectional density of a projectile is divided by its coefficient of form (form factor in commercial small arms jargon³); it yields the projectile's ballistic coefficient.⁴ Sectional density has the same (implied) units as the ballistic coefficient.

Within terminal ballistics, the sectional density of a projectile is one of the determining factors for projectile penetration. The interaction between projectile (fragments) and target media is however a complex subject. A study regarding hunting bullets shows that besides sectional density several other parameters determine bullet penetration.⁵⁶⁷

If all other factors are equal, the projectile with the greatest amount of sectional density will penetrate the deepest.

Metric units

When working with ballistics using SI units, it is common to use either grams per square millimeter or kilograms per square centimeter. Their relationship to the base unit kilograms per square meter is shown in the conversion table above.

Grams per square millimeter

Using grams per square millimeter (g/mm2), the formula then becomes:

S D g / mm 2 = 4 m g π ⋅ d mm 2 {\displaystyle SD_{{\text{g}}/{\text{mm}}^{2}}={\frac {4m_{\text{g}}}{{\pi \cdot d_{\text{mm}}}^{2}}}}

Where:

• SDg/mm2 is the sectional density in grams per square millimeters
• mg is the mass of the projectile in grams
• dmm is the diameter of the projectile in millimeters

For example, a small arms bullet with a mass of 10.4 grams (160 gr) and having a diameter of 6.70 mm (0.264 in) has a sectional density of:

4 · 10.4 / (π·6.72) = 0.295 g/mm2

Kilograms per square centimeter

Using kilograms per square centimeter (kg/cm2), the formula then becomes:

S D kg / cm 2 = 4 m kg π d cm 2 {\displaystyle SD_{{\text{kg}}/{\text{cm}}^{2}}={\frac {4m_{\text{kg}}}{{\pi d_{\text{cm}}}^{2}}}}

Where:

• SDkg/cm2 is the sectional density in kilograms per square centimeter
• mg is the mass of the projectile in grams
• dcm is the diameter of the projectile in centimeters

For example, an M107 projectile with a mass of 43.2 kg and having a body diameter of 154.71 millimetres (15.471 cm) has a sectional density of:

4 · 43.2 / (π·154.712) = 0.230 kg/cm2

English units

In older ballistics literature from English speaking countries, and still to this day, the most commonly used unit for sectional density of circular cross-sections is (mass) pounds per square inch (lbm/in2) The formula then becomes:

S D lb / in 2 = 4 m lb π ⋅ d in 2 = 4 m gr π ⋅ 7000 d in 2 {\displaystyle SD_{{\text{lb}}/{\text{in}}^{2}}={\frac {4m_{\text{lb}}}{{\pi \cdot d_{\text{in}}}^{2}}}={\frac {4m_{\text{gr}}}{\pi \cdot 7000\,{d_{\text{in}}}^{2}}}} ⁸⁹¹⁰ S D l b s / s q i n = 4 ⋅ m l b π ⋅ d i n 2 = 4 ⋅ m g r π ⋅ 7000 d i n 2 {\displaystyle SD_{\mathrm {lbs/sqin} }={\frac {4\cdot m_{\mathrm {lb} }}{{\pi \cdot d_{\mathrm {in} }}^{2}}}={\frac {4\cdot m_{\mathrm {gr} }}{\pi \cdot 7000\,{d_{\mathrm {in} }}^{2}}}}

where:

• SD is the sectional density in (mass) pounds per square inch
• the mass of the projectile is:
  • mlb in pounds
  • mgr in grains
• din is the diameter of the projectile in inches

The sectional density defined this way is usually presented without units. In Europe the derivative unit g/cm2 is also used in literature regarding small arms projectiles to get a number in front of the decimal separator.

As an example, a bullet with a mass of 160 grains (10.4 g) and a diameter of 0.264 in (6.7 mm), has a sectional density (SD) of:

4·(160 gr/7000) / (π·0.264 in2) = 0.418 lbm/in2

As another example, the M107 projectile mentioned above with a mass of 95.2 pounds (43.2 kg) and having a body diameter of 6.0909 inches (154.71 mm) has a sectional density of:

4 · (95.24) / (π·6.09092) = 3.268 lbm/in2

See also

• Ballistic coefficient

References

1. Les étranges obus du fort de Neufchâteau (in French) http://derelicta.pagesperso-orange.fr/aubin3.htm ↩

2. Wound Ballistics: Basics and Applications https://books.google.com/books?id=q4jzcfLhBcYC&dq=sectional+density+cross+sectional+area&pg=PA203 ↩

3. Hornady Handbook of Cartridge Reloading: Rifle, Pistol Vol. II (1973) Hornady Manufacturing Company, Fourth Printing July 1978, p505 ↩

4. Bryan Litz. Applied Ballistics for Long Range Shooting. ↩

5. "Shooting Holes in Wounding Theories: The Mechanics of Terminal Ballistics". Archived from the original on 2021-06-24. Retrieved 2009-07-25. https://web.archive.org/web/20210624031342/https://rathcoombe.net/sci-tech/ballistics/wounding.html ↩

6. MacPherson D: Bullet Penetration—Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma. Ballistics Publications, El Segundo, CA, 1994. ↩

7. Schultz, Gerard. "Sectional Density - A Practical Joke?". Archived from the original on 2023-01-15. https://web.archive.org/web/20230115024756/http://www.gsgroup.co.za/articlesd.html ↩

8. The Sectional Density of Rifle Bullets By Chuck Hawks http://www.chuckhawks.com/sd.htm ↩

9. Sectional Density and Ballistic Coefficients http://www.jbmballistics.com/ballistics/topics/secdens.shtml ↩

10. Sectional Density for Beginners By Bob Beers http://www.chuckhawks.com/sd_beginners.htm ↩