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Franklin to Coulomb Converter

Enter a charge value and pick the direction to convert between franklins and coulombs.

Result

4.803205 × 10⁻¹⁰ Fr
1 C = 2.997925 × 10⁹ Fr
1 Fr = 3.335641 × 10⁻¹⁰ C

How it is calculated

Enter a charge and choose the direction. The conversion uses one fixed factor between the franklin (Fr, also called the statcoulomb) and the coulomb (C):

1 Fr = 3.335640951982 × 10−10 C

In Franklin → Coulomb mode the tool computes C = Fr × 3.335640951982×10−10. In Coulomb → Franklin mode it computes Fr = C ÷ 3.335640951982×10−10. Results are printed in scientific notation with six decimals in the mantissa, such as 4.803205 × 10⁻¹⁰, using the decimal mark of the page language. The tool also lists the rate in both directions, where 1 C is about 2.997925×109 Fr. Zero and negative charges are accepted, and the sign is carried through. Values can be typed in scientific form like 1.6e-19.

Worked example

What is the elementary charge, 1.602176634e-19 C, in franklins? Set the direction to Coulomb → Franklin.

  1. Divide by the factor: 1.602176634×10−19 ÷ 3.335640951982×10−10.
  2. The mantissas give 1.602177 ÷ 3.335641 ≈ 0.48032, and the exponents give 10−19+10 = 10−9.
  3. Combine: 0.48032 × 10−9 = 4.8032 × 10−10.

The tool displays 4.803205 × 10⁻¹⁰ Fr, the value usually quoted for the electron charge in Gaussian (CGS) units.

Try this example →

Common mistakes

  • Choosing the wrong direction. Typing a charge in coulombs while the mode is Franklin → Coulomb multiplies by 3.3×10−10 instead of dividing and gives a number about 1019 times too small.
  • Misreading the exponent. The output 4.803205 × 10⁻¹⁰ is a very small number, not 4.8 times ten.
  • Typing a number with a decimal comma or with spaces. Use a decimal point and, for very small or large values, the e form such as 1.6e-19.
  • Assuming the franklin is a SI-based unit, so that it can be mixed directly into coulomb-based formulas. Gaussian equations such as Coulomb's law have no ε₀, so the same numbers do not drop into SI formulas without converting.
  • Confusing the franklin with the faraday or with ampere-hours. The franklin is a very small charge, about 3.3×10−10 C, whereas those units are enormously larger.

Sources

About this calculator

The franklin (Fr), also called the statcoulomb (statC or esu), is the unit of electric charge in the old CGS-esu (centimeter-gram-second, electrostatic) system of units, defined so that two equal point charges of 1 franklin placed 1 centimeter apart in a vacuum repel each other with a force of exactly 1 dyne. It predates the modern SI system, where charge is measured in coulombs, and the two units relate by the exact factor 1 Fr = 3.335640951982×10⁻¹⁰ C, tied directly to the speed of light through the CGS-to-SI conversion.

This converter switches electric charge between franklins and coulombs in either direction. It's mainly needed by physicists and historians of science reading older electromagnetism literature — many 19th and early 20th-century papers, and some physics textbooks that still favor Gaussian/CGS units for elegance in Maxwell's equations, report charge in franklins or statcoulombs, and converting them to coulombs is necessary to compare with modern SI-based results.

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Comments (1)

  • Editorial team

    Gaussian CGS formulas drop the 4π times epsilon-zero factor, so Coulomb's law there reads force equals q1 q2 over r squared, in dynes. That means converting only the charge is not enough to port a textbook formula: distances and forces must move to the same system too. Do you use this for old physics texts or for checking your own homework problems?

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