---
title: "Oil drops: finding a charge unit in falling times"
description: "Why is one suspended drop not enough to establish an elementary charge?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/millikan-oil-drop-charge-inference/"
language: "en"
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  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/millikan-oil-drop-charge-inference/"
last_modified: "2026-10-15"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Oil drops: finding a charge unit in falling times

Sandbox Physics · 2026-10-15

Why is one suspended drop not enough to establish an elementary charge?

## The microscope sees a trajectory, not a charge

The observer never sees a charge, only a moving drop. A lit oil drop drifts between two capacitor plates, and the observer times it between marked lines, first as it falls under gravity and then with the electric field switched on. The data are distances, times, voltages and the surrounding conditions. The charge has to be worked out with a mechanical model.

A drop held still shows only that the electric force can balance its effective weight. The microscope does not show the drop’s mass. Its size comes from how fast it falls with the field off, and the charge estimate then needs the oil density, the air viscosity and buoyancy. Calling the balanced drop a direct reading of one electron hides all of these steps.

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan

## Balancing weight against drag, and what that assumes

When a spherical drop falls at its terminal speed, its weight minus buoyancy equals the viscous drag, as the equation below states. The two densities are those of oil and air, and the viscosity is that of air. The slip correction is a dimensionless factor that divides the continuum Stokes drag.

The balance holds only for steady motion at low Reynolds number; it does not describe a drop that is accelerating or evaporating. Once the field is on and the electric force points upward, its size follows from the effective weight and the drag acting against it. Its direction has to be known before the inferred charge can be given a sign.

$$
\frac{4\pi r^3}{3}(\rho_{\mathrm{oil}}-\rho_{\mathrm{air}})g=\frac{6\pi\eta r v_{\mathrm{fall}}}{C_{\mathrm{slip}}}
$$

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan

## Watching one drop change charge is a stronger test

A drop can gain or lose charge while staying, to a good approximation, the same object with the same mass. Comparing its rise speeds before and after each change separates the charge step from the unknown mass. Millikan followed such sequences and also compared many different drops; the 1913 paper gives complete series for 58 drops.

A common unit is convincing only if many charges and charge steps all come out as multiples of it within the experimental uncertainty. One drop carrying an unknown number of electrons cannot reveal the unit on its own. A small enough divisor will always make the numbers look like near multiples, so the resolution, the scatter and the size of the observed steps all matter.

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan CaltechAUTHORS, Millikan’s 1913 charge paper — institutional record

## The gas is part of the experiment

With uncorrected Stokes drag, Millikan found that the charge unit he inferred depended on the size of the drop. Once a drop is small enough that the molecular nature of air matters, the air can no longer be treated as a continuous fluid right up to the drop’s surface. Running at different pressures exposed this effect and let him estimate the correction.

Viscosity and temperature enter every inferred size and charge. Brownian motion adds random jitter, and a drop that changes size or is lost from view can spoil a whole sequence. Tight scatter among repeated readings cannot rule out a calibration error they all share. Getting the same unit from drops of different sizes and at different pressures is a separate check, and timing the same motion more often cannot replace it.

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan

## Discrete charge and its exact value are separate questions

The evidence shows a common charge unit across the drops and charge changes studied. It says nothing about the shape of the electron, and it did not survey every possible carrier of charge. The mechanics behind the inference can stay classical; the charge pattern it uncovers is discrete.

Today’s SI fixes the numerical value of the elementary charge by definition, but a droplet measurement still has an uncertainty. A modern experiment tests its apparatus and how well it realizes the units. The 1913 measurement estimated a constant with the unit conventions and calibrations available then.

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan NIST, Defining the International System of Units — the 2019 ampere definition

## Two Millikan measurements answer different questions

The oil-drop experiment supplies the charge scale needed to read the slope of the photoelectric stopping potential against frequency. The photoelectric experiment then tests how electron energy depends on light frequency. Both involve a voltage, but neither can stand in for the other.

The linked oil-drop Lab generates simulated camera tracks with the field off and on, and estimates each charge as a continuous number without rounding to an integer. It shows how the inference works under a given drag and diffusion model, so it cannot establish quantization on its own. A historical test of a common charge unit would need the actual timings, corrections, rejected runs and uncertainties.

Read the evidence: R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan Robert A. Millikan — official 1923 award facts

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Oil-drop measurement: infer continuous charge from recorded motion](https://sandboxphysics.com/labs/oil-drop-charge/)

## Sources and reading notes

The APS scan of Millikan’s 1913 paper is readable, including the drag correction and the tables for repeated drops. Caltech holds a library entry for the paper, and NIST explains the modern SI definition. This article follows the reasoning published in the paper; it does not examine laboratory notebooks or refit the data.

1. [R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan](https://journals.aps.org/pr/pdf/10.1103/PhysRev.7.355)
2. [R. A. Millikan (1913), On the Elementary Electrical Charge and the Avogadro Constant, Phys. Rev. 2, 109–143 — original scan](https://journals.aps.org/pr/pdf/10.1103/PhysRev.2.109)
3. [CaltechAUTHORS, Millikan’s 1913 charge paper — institutional record](https://authors.library.caltech.edu/records/sfc90-k2g07)
4. [NIST, Defining the International System of Units — the 2019 ampere definition](https://www.nist.gov/nist-museum/defining-international-system-units-si)
5. [Robert A. Millikan — official 1923 award facts](https://www.nobelprize.org/prizes/physics/1923/millikan/facts/)

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