How big is the mass change from charging a typical smartphone battery in grams and scientific notation?
Executive summary
A fully charged smartphone battery gains an amount of mass so vanishingly small that it is undetectable in ordinary measurement: published community calculations and popular summaries put the increase in the neighborhood of trillionths-to-billionths of a gram — commonly reported as something like 10^-12 to 10^-9 grams (scientific notation) depending on the assumed battery energy [1] [2]. Physically this follows from mass–energy equivalence (E = mc^2) and is significant only as a theoretical curiosity, not as a practical weight change anyone could measure with shop or postal scales [1] [3].
1. Why the question comes up: mass–energy equivalence and batteries
The idea that a charged battery might weigh more springs from Einstein’s E = mc^2 — add energy to a system, and the system’s inertial mass increases by E/c^2 — and that argument is explicitly invoked in community discussions about phone batteries [1]. Popular and technical forum threads summarize the physics the same way: charging stores energy in chemical potential differences and, in principle, raises the battery’s mass by the equivalent amount of energy divided by c^2 [1] [4]. That conceptual point is uncontested among the sources: energy has mass in relativity even when the practical effect is negligible [1].
2. What the published estimates say: numbers people quote
Community calculations and secondary summaries converge on a vanishingly small number. One forum post that walks through a back‑of‑the‑envelope example (50 watt‑hours ≈ 180,000 joules) reports a mass increase of order 10^-12 to 10^-9 grams, with one commonly cited figure being “about 2 picograms” for a 50 Wh store [1]. A commercial explainer likewise states that controlled calculations translate to changes “in the range of trillionths of a gram” and says a fully charged typical cell’s added mass is less than a billionth of a gram [2]. Broad physics answers on Stack Exchange and similar forums emphasize the same takeaways: the increase exists in principle but is undetectably small [3] [4].
3. Why different sources give slightly different powers of ten
The spread in reported exponents comes from what energy value is assumed for “a smartphone battery” and from rounding in the quick E/c^2 arithmetic; different authors use different nominal capacities (milliamp‑hours or watt‑hours) and reporting styles (picograms, trillionths, or billionths of a gram) so estimates land anywhere between roughly 10^-12 and 10^-9 grams in the cited material [1] [2]. Forum and Stack Exchange answers repeatedly warn that experimental detection is essentially impossible because production tolerances and measurement noise in real batteries are many orders of magnitude larger than these theoretical mass shifts [3] [5].
4. What that means in grams and scientific notation
The cited reporting frames the answer as: on the order of a trillionth of a gram up to a billionth of a gram — written in scientific notation that’s roughly 1×10^-12 g to 1×10^-9 g, with several popular estimates clustered near 10^-12–10^-11 g [1] [2]. All sources agree this is far below any practical detection limit and that the difference is a theoretical consequence of added stored energy rather than any mechanical or manufacturing mass change [3] [4].
5. Limits of the reporting and remaining caveats
The available community and popular pieces do not present a formal peer‑reviewed experimental measurement of this exact effect for a specific smartphone model, and the numerical ranges reported depend on assumed battery capacity and rounding choices [1] [2]. The sources make clear the point is conceptual rather than operational: while relativity predicts a mass change tied to stored energy, the change is many orders of magnitude below measurement noise or manufacturing variation, and some battery chemistries (e.g., systems that exchange atmospheric oxygen) introduce chemical‑mass bookkeeping complexities that can reverse intuitive expectations [1].
6. Bottom line
A practical, evidence‑backed summary from the collected reporting is that charging a typical smartphone battery increases its mass by an amount on the order of 10^-12 to 10^-9 grams — in scientific notation, roughly 1×10^-12 g to 1×10^-9 g — a theoretically real but experimentally negligible change [1] [3] [2] [4].