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Femto- — Definition, Formula & Examples

Femto- is a metric prefix that means one quadrillionth, or 10−1510^{-15}. Its symbol is a lowercase **f**, so one femtometer is written as 1 fm.

In the International System of Units (SI), femto- denotes a factor of 10−1510^{-15}. Adopted in 1964, it derives from the Danish/Norwegian word "femten," meaning fifteen, reflecting the power of ten it represents.

Key Formula

1  f(unit)=10−15  (unit)1\;\text{f(unit)} = 10^{-15}\;\text{(unit)}
Where:
  • f\text{f} = The femto- prefix symbol
  • 10−1510^{-15} = One quadrillionth, the scaling factor

How It Works

Attach femto- to any base unit to divide that unit by 101510^{15}. For example, 1 femtosecond (fs) equals 10−1510^{-15} seconds. To convert from femto-units to the base unit, multiply by 10−1510^{-15}. To convert from the base unit to femto-units, multiply by 101510^{15}. Femto- sits one step below pico- (10−1210^{-12}) and one step above atto- (10−1810^{-18}) on the metric prefix ladder.

Worked Example

Problem: A proton has a diameter of about 1.7 femtometers (fm). Express this in meters.
Step 1: Replace the prefix femto- with its factor of 10−1510^{-15}.
1.7  fm=1.7×10−15  m1.7\;\text{fm} = 1.7 \times 10^{-15}\;\text{m}
Step 2: Compare to picometers: since 1  pm=10−12  m1\;\text{pm} = 10^{-12}\;\text{m}, divide by 10−1210^{-12}.
1.7×10−15  m=0.0017  pm1.7 \times 10^{-15}\;\text{m} = 0.0017\;\text{pm}
Answer: The proton's diameter is 1.7×10−151.7 \times 10^{-15} m, or 0.0017 pm.

Why It Matters

Femtosecond lasers are used in eye surgery and ultrafast chemistry, where scientists study reactions that happen in quadrillionths of a second. Nuclear physicists routinely measure distances in femtometers because that is the scale of protons and neutrons.

Common Mistakes

Mistake: Confusing femto- (10−1510^{-15}) with pico- (10−1210^{-12}) because both describe extremely small quantities.
Correction: Remember that femto- is 1,000 times smaller than pico-. On the prefix ladder, pico → femto means dividing by an additional 10310^{3}.

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