We have measured the

\frac{1}{f}

voltage noise in continuous metal films. At room temperature, samples of pure metals and bismuth (with a carrier density smaller by

10^{5}

) of similar volume had comparable noise. The power spectrum

S_{V} (f)

was proportional to

\frac{{\bar{V}}^{2}}{Ω f^{γ}}

, where

\bar{V}

is the mean voltage across the sample,

Ω

is the sample volume, and

1.0 ≲ γ ≲ 1.4

\frac{S_{V} (f)}{{\bar{V}}^{2}}

was reduced as the temperature was lowered. Manganin, with a temperature coefficient of resistance (

β

) close to zero, had no discernible noise. These results suggest that the noise arises from equilibrium temperature fluctuations modulating the resistance to give

S_{V} (f) \propto \frac{{\bar{V}}^{2} β^{2} k_{B} T^{2}}{C_{V}}

, where

C_{V}

is the total heat capacity of the sample. The noise was spatially correlated over a length

λ (f) \approx {(\frac{D}{f})}^{\frac{1}{2}}

, where

D

is the thermal diffusivity, implying that the fluctuations obey a diffusion equation. The usual theoretical treatment of spatially uncorrelated temperature fluctuations gives a spectrum that flattens at low frequencies in contradiction to the observed spectrum. However, the empirical inclusion of an explicit

\frac{1}{f}

region and appropriate normalization lead to

\frac{S_{V} (f)}{{\bar{V}}^{2}} \propto \frac{β^{2} k_{B} T^{2}}{C_{V}} [3 + 2 \ln (\frac{l}{w})] f

, where

l

is the length and

w

is the width of the film, in excellent agreement with the measured noise. If the fluctuations are assumed to be spatially correlated, the diffusion equation can yield an extended

\frac{1}{f}

region in the power spectrum. We show that the temperature response of a sample to

δ

- and step-function power inputs has the same shape as the autocorrelation function for uncorrelated and correlated temperature fluctuations, respectively. The spectrum obtained from the cosine transform of the measured step-function response is in excellent agreement with the measured

\frac{1}{f}

voltage noise spectrum. Spatially correlated equilibrium temperature fluctuations are not the dominant source of

\frac{1}{f}

noise in semiconductors and discontinuous metal films. However, the agreement between the low-frequency spectrum of fluctuations in the mean-square Johnson-noise voltage and the resistance fluctuation spectrum measured in the presence of a current demonstrates that in these systems the

\frac{1}{f}

noise is also due to equilibrium resistance fluctuations.

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