The Millikan Oil Drop Experiment: Weighing the Electron

Robert Millikan suspended tiny drops of oil between two electrically charged metal plates at the University of Chicago between 1909 and 1913, watching each drop drift upward or downward in response to gravity and electric force. By measuring the voltage needed to hold a drop perfectly still, he calculated the electric charge carried by that drop. Every drop carried a charge that was a whole-number multiple of the same tiny value: the elementary charge, 1.592 × 10⁻¹⁹ coulombs, within half a percent of today's accepted value of 1.602 × 10⁻¹⁹ coulombs.

The Problem in 1909: How Big Is a Single Unit of Charge?

By 1900, physicists were confident that electric charge comes in discrete units — that you cannot have half an electron's worth of charge any more than you can have half a proton. J.J. Thomson had identified the electron in 1897, and Faraday's earlier work on electrolysis had implied a natural unit of charge. But no one had measured that unit directly with precision.

The available methods were indirect. Faraday's law of electrolysis lets you calculate the charge-to-mass ratio of ions, not the absolute charge. Thomson's measurement of the electron's charge-to-mass ratio in cathode ray experiments gave e/m, but converting that to e alone required knowing the electron's mass independently, which was uncertain. Various estimates of the elementary charge by 1900 ranged across more than an order of magnitude.

What was needed was an experiment that could catch individual charges in the act — that could watch a single charged particle and measure the force on it. Millikan's apparatus was the first to do this reliably.

Elementary charge (e) — the smallest unit of electric charge found in nature under ordinary conditions, equal to approximately 1.602 × 10⁻¹⁹ coulombs. All observable electric charges are whole-number multiples of this value.

Source: American Physical Society News — "August 1913: Robert Millikan Reports His Oil Drop Results" (aps.org/apsnews/2006/08/robert-millikan-oil-drop-results)

An Earlier Attempt: Why Water Drops Failed

Before the famous oil drop apparatus, Millikan and his students worked with charged water droplets. The principle was the same: ionize air in a chamber, let charged droplets form, apply an electric field. But water drops had a fatal practical flaw — they evaporated too quickly. A droplet would shrink during the observation, changing its mass and therefore its terminal velocity, making any calculation of charge ambiguous.

Millikan's graduate student Harvey Fletcher suggested switching to oil. Oil is nearly non-volatile at room temperature: an oil droplet suspended in a sealed chamber retains its mass for minutes or longer without measurable evaporation. This single substitution transformed an impractical experiment into a workable one. Fletcher used a simple perfume atomizer to produce the fine mist of oil droplets. The switch to oil was Fletcher's contribution, and it was the enabling step that made the experiment function.

Source: Physics Today — "Remembering the oil-drop experiment" (physicstoday.aip.org/features/remembering-the-oil-drop-experiment)

Source: Harvey Fletcher's account — "My work with Millikan on the oil-drop experiment" (physics.byu.edu/docs/publication/2250)

The Apparatus: Balancing Gravity Against Electricity

The working apparatus was built in the Ryerson Physical Laboratory at the University of Chicago. Its key components were simple in principle, demanding in execution.

Two horizontal brass plates separated by approximately 16 mm formed the capacitor. The plates could be charged to a voltage of several thousand volts by a battery and a voltage divider, creating a roughly uniform electric field between them. The top plate was connected to the positive terminal and the bottom to the negative terminal, producing an upward electric force on negatively charged droplets.

An atomizer (essentially a perfume spray bottle) forced a jet of air through a small hole in the side of the apparatus, carrying oil droplets into the chamber above the top plate. Some of these droplets fell through a small hole in the top plate and entered the space between the plates.

An X-ray source or radioactive material ionized the air between the plates, allowing droplets to pick up charge by capturing ions. The amount of charge on a given drop varied randomly and could change during an observation if the drop captured another ion.

A calibrated microscope allowed Millikan to watch individual droplets from the side and measure their velocity — upward or downward — against a ruled scale. The magnification and scale factor were calibrated against a micrometer.

A stopwatch timed the droplet's transit across known distances in the field of view.

Parameter	Value
Plate separation	~16 mm
Applied voltage range	Up to ~10,000 V
Oil used	Clockmaker's oil (non-volatile)
Observation method	Calibrated microscope, side view
Ionization source	X-rays or radium
Plate material	Brass

Source: Britannica — "Millikan oil-drop experiment" (britannica.com/science/Millikan-oil-drop-experiment)

The Measurement Logic: Four Forces on One Drop

The physics of the measurement involves balancing four forces on each droplet. Understanding the logic makes the method's power clear.

Gravity pulls the droplet downward with force F_g = mg, where m is the mass of the drop and g is gravitational acceleration (9.8 m/s²).

Air resistance (viscous drag) opposes the droplet's motion. For a sphere moving slowly through a viscous fluid, this force is given by Stokes's law: F_drag = 6πηrv, where η is the viscosity of air, r is the droplet radius, and v is the velocity. This law was well-established from 19th-century fluid mechanics.

Buoyancy partially offsets gravity, since the droplet is denser than air but not infinitely so. Millikan corrected for buoyancy in his calculations.

Electric force from the applied field: F_E = qE, where q is the charge on the drop and E is the electric field strength (voltage divided by plate separation).

Millikan used two different experimental conditions for each drop. First, with the electric field off, the drop fell freely under gravity and drag, reaching a constant terminal velocity v_f when the drag force exactly balanced gravity minus buoyancy. From v_f and Stokes's law, he could calculate the drop's radius r, and from r and the known density of oil, he could calculate the mass m.

Second, with the field on, Millikan adjusted the voltage until the drop hung motionless — perfectly balanced between the upward electric force and the downward gravitational force. At this point, qE = mg (corrected for buoyancy). Since E = V/d (voltage divided by plate separation), and he now knew m from the first measurement, he could solve directly for q.

This is like weighing an invisible package by finding the counterweight that exactly balances it on a scale: you don't need to know what the package looks like, only how much push is needed to hold it up.

Source: Wikipedia — "Oil drop experiment" (en.wikipedia.org/wiki/Oil_drop_experiment)

The Results: A Discrete Ladder of Charges

Over the course of thousands of measurements on hundreds of individual oil droplets — different sizes, different amounts of charge picked up from the ionized air — Millikan observed a consistent pattern. The charge on every droplet was an integer multiple of a single base value. He never measured a fractional charge — a drop with 1.5 units, or 2.3 units. The charges were always n × e for some whole number n: 1e, 2e, 3e, 4e, and so on.

This was the first direct demonstration that electric charge is quantized — that it comes in indivisible packets. Each packet is the elementary charge carried by a single electron. A drop with charge 3e had captured three excess electrons from the ionized air.

In his seminal 1913 paper in Physical Review, Millikan reported the elementary charge as e = 4.774 × 10⁻¹⁰ electrostatic units (ESU), with an uncertainty of roughly 0.2%. In SI units, this translates to approximately 1.592 × 10⁻¹⁹ coulombs — about 0.6% below the modern accepted value of 1.602 × 10⁻¹⁹ coulombs.

Source: Gizmodo — "Did a Case of Scientific Misconduct Win the Nobel Prize for Physics?" (gizmodo.com/did-a-case-of-scientific-misconduct-win-the-nobel-prize-1565949589)

Source: APS — "Physics Landmarks: Millikan Measures the Electron's Charge" (physics.aps.org/articles/v5/9)

The precision was remarkable for 1913. The main source of systematic error was the viscosity of air, which Millikan had to measure carefully and correct for using refinements to Stokes's law that account for the fact that Stokes's law becomes inaccurate when the droplet radius approaches the mean free path of air molecules. This correction — the Cunningham correction factor — was itself a minor piece of physics that Millikan had to work out.

The Controversy: Felix Ehrenhaft and Data Selection

Not everyone accepted Millikan's result immediately. Felix Ehrenhaft, an Austrian physicist, ran similar experiments and reported measurements that he claimed showed charge values smaller than e — what he called "subelectrons." The dispute between Millikan and Ehrenhaft ran through the 1910s, with genuine bitterness on both sides.

Ehrenhaft's claims were ultimately wrong. His measurements of very small particles were contaminated by systematic errors, including non-spherical droplets and impurities that violate the assumptions of Stokes's law. When the apparatus is pushed to measure very small charges on very small particles, the Stokes's law correction becomes unreliable, and the discreteness of charge is harder to establish cleanly. Ehrenhaft's "subelectrons" were measurement artifacts.

Source: University of Michigan — "The Oil Drop Experiment: A Rational Reconstruction" (websites.umich.edu/~chemstu/content_weeks/F_06_Week4/Mullikan_Erenhaft.pdf)

However, the controversy about Millikan's own data did not fully emerge until decades later. In 1982, historians examining Millikan's lab notebooks found extensive notation alongside his measurements — comments like "beauty," "good," "perfect," and also "excluded" and "won't publish." Millikan had not included all his measurements in his published analysis. His papers present 58 measurements; his notebooks contain 175 runs.

The accusation of data selection — choosing measurements that gave consistent results and discarding others without explicit scientific justification — has made the oil drop experiment a standard case study in the ethics of experimental physics. The defense is that Millikan was doing legitimate data quality assessment: experienced experimenters routinely discard runs where something clearly went wrong (a vibration, a sudden voltage fluctuation, a suspected multi-droplet event). The prosecution's argument is that Millikan's selection criteria correlated with whether the result agreed with his emerging value for e — which is selection bias, not quality control.

The debate remains genuinely unresolved in the history of science. What is agreed upon is that Millikan's final published value was accurate to within 0.6% of the true value, that his analysis method was sound, and that his result was reproducible by other groups who did not use his specific data. Whether his data selection practices were acceptable science or misconduct is a judgment call that depends on how strictly you apply norms that were only partly articulated in his era.

Source: Quora — "Why didn't Fletcher get credit in the oil drop experiment?" (quora.com/Why-didnt-Fletcher-get-credit-in-the-oil-drop-experiment)

Harvey Fletcher and the Question of Credit

The data selection controversy is not the only ethical dimension of the oil drop experiment. Harvey Fletcher, Millikan's graduate student and the person who suggested switching to oil and who built and operated much of the apparatus, published only one paper in his own name on this work: a paper on the measurement of charge using the apparatus he had helped design. The landmark 1913 paper presenting the elementary charge result bore Millikan's name alone.

According to documents found after Fletcher's death, Millikan had told Fletcher that he could be sole author of a paper on a related topic — the Brownian motion of oil droplets — in exchange for yielding sole authorship of the elementary charge paper to Millikan. Fletcher complied; Millikan used his authority as PhD supervisor to structure the agreement. Fletcher went on to a distinguished career at Bell Laboratories in communication acoustics, but the Nobel Prize in 1923 went to Millikan alone, partly for the oil drop work.

Fletcher wrote about the arrangement late in his life, concluding that while he felt it was unfair, he understood Millikan's reasoning that the discovery was important enough for one name rather than two, and that his own career had flourished regardless. The case is now taught regularly in courses on scientific ethics as an example of the power differential between faculty and students and the institutional norms that were (and arguably still are) inadequate to protect graduate student contributions.

Source: Online Ethics Center — "The Millikan Case: Discrimination Versus Manipulation of Data" (onlineethics.org/cases/ethics-science-classroom/millikan-case-discrimination-versus-manipulation-data)

A Timeline of the Oil Drop Experiment

Year	Event
1897	J.J. Thomson identifies the electron; measures e/m ratio
1907	Millikan begins cloud chamber experiments with water droplets
1909	Fletcher suggests oil; first successful oil drop observations
Dec 1909	Millikan and Fletcher begin systematic oil drop measurements
1910	First results published in Science
1913	Millikan's landmark paper in Physical Review: e = 4.774 × 10⁻¹⁰ ESU
1913–1920	Ehrenhaft dispute over claimed subelectron charges
1923	Millikan receives Nobel Prize in Physics
1982	Historians publish analysis of Millikan's notebooks; data selection controversy begins
2003	Fletcher's autobiographical account published posthumously
2019	Modern accepted value: e = 1.602176634 × 10⁻¹⁹ C (exact, by SI redefinition)

The Stokes's Law Correction: Why Getting Viscosity Right Mattered

The main systematic error in the oil drop experiment came from applying Stokes's law — a formula derived for spheres moving through a continuous fluid — to droplets small enough that the molecular nature of air becomes relevant. Stokes's law assumes the surrounding medium is a continuous fluid. For very small spheres (radius comparable to the mean free path of air molecules, which is about 68 nm at standard pressure), the air molecules interact with the sphere differently from a continuous fluid, and the actual drag force is smaller than Stokes's law predicts.

Millikan applied a correction factor derived by E.H. Cunningham in 1910: the corrected drag force is F_drag = 6πηrv / (1 + A·λ/r), where λ is the mean free path of air and A is a dimensionless constant close to 0.9. This correction is small for large drops (r >> λ) but significant for the smallest drops Millikan observed.

Getting this correction right was critical to the accuracy of the final result. Millikan's own measurements at different air pressures allowed him to determine the constant A empirically, making his result self-consistent across a range of drop sizes. This was good experimental practice: by varying the pressure (which changes λ), he could check that the same value of e emerged regardless, and use the consistency as a constraint on systematic errors.

Source: SATHEE Physics — "Millikan Oil Drop Experiment" (sathee.iitk.ac.in/article/physics/physics-millikan-oil-drop-experiment/)

What the Experiment Proved Beyond the Charge Value

The numerical value of e, however important, was not the experiment's deepest result. The deeper result was the demonstration that charge is quantized — that nature has chosen a minimum unit of electric charge and does not subdivide it.

This was not obvious in 1909. Classical electromagnetism is perfectly consistent with a universe where charge is continuous — where you can have any real-number amount of charge, including 1.37 or 0.0042 units. The oil drop experiment showed that this is not the world we live in. Every charged drop had a charge of n × (1.592 × 10⁻¹⁹ C) for some positive integer n. The histogram of measured charges showed discrete peaks at integer multiples of e, not a continuous distribution.

Charge quantization is one of the fundamental empirical facts of physics, and it remains unexplained by the Standard Model of particle physics in the sense that the theory requires it as an input rather than deriving it from deeper principles. (In Grand Unified Theories and in string theory, charge quantization emerges more naturally, but these frameworks remain unconfirmed experimentally.) Millikan's result is the direct observational foundation for this fact.

Source: Medium — "The Millikan Oil Drop Experiment to Determine the Charge of an Electron" by Rhett Allain (rjallain.medium.com/the-millikan-oil-drop-experiment-to-determine-the-charge-of-an-electron-351f144545d2)

The Modern Value and the Redefined SI

In 2019, the International System of Units was redefined so that the elementary charge e is now an exact defined value: e = 1.602176634 × 10⁻¹⁹ coulombs, exactly. The ampere — the unit of electric current — is now defined in terms of e, rather than e being derived from the ampere. This means the question "what is the charge of the electron?" no longer has an experimental answer in the new SI: it has a definitional one.

This redefinition does not diminish Millikan's achievement. The value selected for the definition was determined by decades of progressively more precise measurements using descendants of his technique, along with complementary methods including Josephson junction measurements and quantum Hall effect measurements. The number written into the 2019 SI definition is the best measured value of e available at the time of the redefinition, traceable directly to experimental efforts that began with Millikan's glass plates and stopwatch in Chicago.

Source: Vedantu — "Millikan's Oil Drop Experiment: Charge of Electron and Discovery" (vedantu.com/chemistry/millikans-oil-drop-experiment)

What People Get Wrong About This Experiment

A common simplification in textbooks is that Millikan simply "measured the charge of the electron." More precisely, he measured the minimum unit of charge carried by oil droplets ionized by X-rays — demonstrating that this minimum is quantized and measuring its value. The connection to electrons required the assumption that the charge carriers produced by X-ray ionization are electrons (or, more accurately, that an ionized air molecule has lost or gained one or more electrons). This was a well-supported assumption in 1913 but was still an assumption.

Another common error is treating the experiment as definitive proof of charge quantization on its own. The experiment provides extremely strong evidence that oil drops carry charges in integer multiples of e. It does not directly prove that fractional charges (like those of quarks, which carry ±1/3 and ±2/3 e) are impossible in principle — quarks carry fractional charges but do not appear individually in nature. The experiment's scope is bounded by the conditions it tested.

Finally, the textbook presentation usually skips the Cunningham correction and the viscosity measurements, making the experiment sound simpler than it was. The actual precision of Millikan's result depended critically on getting the air viscosity and the Cunningham factor right. The conceptual setup is simple; the experimental execution required careful attention to multiple sources of systematic error simultaneously.

For a related measurement of atomic structure from the same era, see the Rutherford gold foil experiment. For how the electron's properties are understood in modern particle physics, see the Standard Model of particle physics.

FAQs

Q: Why did Millikan use oil instead of water?
A: Water drops evaporate quickly, so their mass changed during the observation, making precise charge calculations impossible. Oil is nearly non-volatile at room temperature and retains its mass for the entire duration of a measurement. The switch from water to oil was suggested by Millikan's graduate student Harvey Fletcher and was the practical key that made the experiment work.

Q: How did Millikan know the drops were carrying electron-sized charges rather than some other particle?
A: Millikan did not prove which particles were responsible for the charge. He demonstrated that the minimum detectable charge unit was always the same value, regardless of which drop was measured or how it was charged. The connection to electrons came from consistency with Thomson's e/m measurements and from the known physics of X-ray ionization, which strips electrons from air molecules. The convergence of evidence from multiple independent methods made the identification compelling.

Q: What is the Cunningham correction and why does it matter?
A: Stokes's law, which describes the drag force on a sphere moving through a fluid, assumes the fluid is continuous. For very small oil drops (radius comparable to the mean free path of air molecules, about 68 nm at sea level), air does not behave as a continuous fluid and the actual drag is less than Stokes's law predicts. The Cunningham correction adds a factor that reduces the calculated drag force. Without this correction, the inferred radius and mass of small droplets would be wrong, and the calculated charge would be systematically off.

Q: Did Millikan really commit scientific misconduct?
A: This is genuinely contested among historians of science. Millikan's lab notebooks show that he excluded many measurements from his final analysis, sometimes with notes suggesting the exclusion was influenced by whether the result agreed with his emerging value. This looks like selection bias. The defense is that experimenters routinely and legitimately exclude measurements where something went wrong, and that Millikan was doing legitimate data quality assessment. The published result was accurate, reproducible, and obtained by sound methods — facts that complicate the misconduct narrative. The case is widely used in science ethics courses precisely because it does not have a clean verdict.

Q: Why is the elementary charge now a defined constant rather than a measured one?
A: In the 2019 SI redefinition, the seven base units were redefined so that fundamental physical constants — including the elementary charge e, Planck's constant h, and the speed of light c — have exact defined values. This eliminates measurement uncertainty in the definitions themselves while requiring that all physical measurements be calibrated against quantum standards. The value chosen for e was determined by the best available experimental data at the time of redefinition.

Q: What was Harvey Fletcher's actual contribution to the experiment?
A: Fletcher suggested using oil instead of water, which was the enabling practical innovation. He built and operated much of the apparatus, conducted many of the measurements, and wrote his doctoral dissertation on the Brownian motion of oil droplets observed during the same experimental sessions. His contribution to the elementary charge measurement was substantial enough that some historians argue he deserved co-authorship on the 1913 paper. Millikan's arrangement — sole authorship of the charge paper for himself, sole authorship of the Brownian motion paper for Fletcher — is now widely considered ethically problematic.

The Takeaway

The Millikan oil drop experiment answered a question that had been implicit in all of 19th-century electricity: how big is the smallest possible unit of charge? The answer — 1.602 × 10⁻¹⁹ coulombs, quantized, never subdivided — is one of the bedrock numbers of physics. Every circuit, every transistor, every electrochemical reaction operates in a world shaped by this discreteness. Millikan measured it with a microscope, a stopwatch, and a spray bottle of oil in 1913, with an accuracy that was not improved significantly for another thirty years. That it came with ethical complications — Fletcher's uncredited contribution, the notebook controversy — does not diminish the physics. It does make the story more honest about how science actually works: precise results achieved by real people navigating real institutional pressures, with consequences that outlast both the credit disputes and the experimenters themselves.

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