The internal resistance calculator above turns a load test into the one number that explains why a battery reads 1.5 V on a meter and only 1.35 V once something is actually connected to it. Every real voltage source behaves as an ideal source in series with a resistance, and that series resistance is where the missing voltage goes. It is what limits how much current a source can deliver, how much of its energy reaches the load, and how hot it gets while doing so.
Arb Digital publishes free physics and electronics calculators built around what you can actually measure. Internal resistance cannot be measured directly with a meter, because putting an ohmmeter across a live source measures nothing useful. It has to be inferred from how the terminal voltage responds to load, and this page supports the three measurement routes people genuinely use, then runs the model forwards once the answer is in hand.
What This Internal Resistance Calculator Does
The first route is the classic single-load test: measure the open-circuit voltage, connect a known resistor, measure the terminal voltage again. The second is the same test where the load is not a simple resistor and you measured current directly instead. The third is the two-point method, which needs no open-circuit reading at all and is the more reliable technique for sources whose EMF drifts while you work. The fourth runs the model in reverse, predicting what terminal voltage a source with a known internal resistance will deliver into a chosen load.
The supporting grid always shows the same four quantities. The terminal voltage is what the load actually sees. The load current follows from that voltage and the load. The power delivered to the load is the useful output. The efficiency is the fraction of the source's total power that reaches the load rather than being burned inside the source, and it equals the terminal voltage divided by the EMF, which makes it easy to sanity-check by eye.
Degenerate inputs get an explanation rather than a NaN. A terminal voltage equal to or above the open-circuit EMF implies a zero or negative internal resistance, which means either the source is not what you think it is or one of the readings is wrong, and the tool says which. A zero load current cannot determine a resistance. Two load points at the same current give a divide-by-zero, and the tool asks for a wider spread instead of returning infinity.
How to Use It
- Take the open-circuit reading first and quickly. Connecting a load changes a cell's chemistry, and the recovered open-circuit voltage after a heavy load is not the same as the one before it.
- Load the source hard enough to see a change. A load that drops the terminal voltage by only a millivolt gives an internal resistance dominated by your meter's resolution. Aim for a sag of several per cent.
- Do not short the source to get a big sag. A short circuit on a lithium cell or a lead-acid battery is dangerous, and the result is not more accurate for it.
- Prefer the two-point method for anything that drifts. Taking two loaded readings in quick succession cancels out a slowly falling EMF; comparing a loaded reading with an open-circuit one taken minutes earlier does not.
- Record the temperature and the state of charge. An internal resistance without those two pieces of context is not comparable with any other measurement of the same cell.
The Formula: How Internal Resistance Is Calculated
Model the source as an ideal EMF ε in series with an internal resistance r. When a current I flows, the terminal voltage is V = ε − Ir. That single equation generates all three measurement routes. Given a current, r = (ε − V) / I. Given a load resistance instead, the current is V/R, so r = R(ε − V) / V. From two load points, the EMF cancels out entirely: r = (V1 − V2) / (I2 − I1). OpenStax University Physics Volume 2, section 10.1 on electromotive force, sets out the same model and works several examples of terminal voltage falling as load increases.
Work the defaults through. A cell measures 1.5 V open-circuit and 1.35 V across a 1 Ω load. The current is 1.35 ÷ 1 = 1.35 A. The voltage lost inside the cell is 1.5 − 1.35 = 0.15 V, so r = 0.15 ÷ 1.35 = 0.111 Ω. The load receives 1.35 × 1.35 = 1.82 W while the cell dissipates 1.35² × 0.111 = 0.203 W internally, so the efficiency is 1.35 ÷ 1.5 = 90 per cent.
The two-point defaults describe the same cell measured at two loads: 1.44 V at 0.6 A and 1.35 V at 1.35 A. The slope is (1.44 − 1.35) ÷ (1.35 − 0.6) = 0.09 ÷ 0.75 = 0.12 Ω, and extrapolating back to zero current gives an EMF of 1.44 + 0.6 × 0.12 = 1.512 V. The small disagreement with the single-load figure is exactly the kind of real-world spread that makes the two-point method worth preferring. HyperPhysics on Ohm's law and Kirchhoff's loop rules covers the circuit reasoning that puts the internal resistance in series in the first place.
Maximum Power Transfer Is Not Maximum Efficiency
This is the most useful non-obvious consequence of internal resistance, and it trips up almost everyone who meets it first in a textbook. The power delivered to the load peaks when the load resistance equals the internal resistance. At that point, though, exactly half the total power is being dissipated inside the source, so the efficiency is 50 per cent. Matching for maximum power and matching for maximum efficiency are opposite goals.
Which one you want depends entirely on whether the energy is scarce. In a radio receiver front end the signal power is minute and the source energy is free, so matching for maximum power transfer is correct and the 50 per cent loss is irrelevant. In a battery-powered device the energy is the whole constraint, and a load resistance many times the internal resistance is what you want, accepting less power in exchange for far higher efficiency and much less self-heating in the cell.
The tool shows this directly. Set the load resistance equal to the internal resistance and watch the power to the load peak while the efficiency reads 50 per cent. Raise the load resistance from there and the power falls while the efficiency climbs. The whole design tension in power delivery is contained in those two columns moving in opposite directions.
Why the Same Battery Gives Different Answers
Internal resistance is not a constant of the cell. It rises steadily as a cell discharges, because the chemistry that supplies the current becomes harder to reach. It rises sharply as temperature falls, which is why a car that starts easily in summer struggles at minus ten: the cranking current is unchanged but the terminal voltage collapses. It rises permanently with age and cycle count, and that rise is one of the more reliable early indicators that a cell is nearing the end of its useful life.
It also depends on how fast you measure. A DC load test like this one includes the slow electrochemical polarisation effects; a short AC pulse at a kilohertz measures only the ohmic component and gives a lower figure. Commercial battery testers usually quote the AC value, so a DC load test result will not match a tester's reading and neither is wrong. If you are comparing measurements, compare like with like.
The practical takeaway is to treat a single internal resistance reading as a snapshot rather than a specification, and to track it over time under consistent conditions. That trend is more informative than any one number. Our battery capacity calculator handles pack energy and configuration, and the battery life calculator estimates runtime at a given draw; neither models the voltage sag that this page measures, which is what determines whether a device browns out before the capacity is used up.
Assumptions and Range of Validity
The model behind this page is deliberately simple: one ideal EMF, one series resistance, both constant during the measurement. That is an excellent approximation for a resistive load at steady state and a poor one everywhere else. It does not capture the frequency dependence of a real cell, which behaves more like a network of resistors and capacitors than a single resistor. It does not capture the recovery that follows removing a load, nor the way lithium chemistries show a markedly different resistance during charge than discharge.
It also assumes your wiring and connections contribute nothing. In practice they contribute a great deal. A corroded terminal, a thin test lead or a poor crocodile clip can add more resistance than the cell itself, and the calculator has no way to tell the difference — it will report their sum and call it internal resistance. For low-resistance cells this is the dominant error source, which is why serious measurements use a four-wire connection with separate sense leads.
Finally, this page publishes no cell, ampacity or circuit-protection ratings of its own, and it makes no judgement about whether a source is safe to load. Do not short-circuit cells to force a large reading. High-current and mains-connected work is designed and signed off by a qualified electrician or electrical engineer against the applicable code; if that is your question, our breaker size calculator and voltage drop calculator are the right starting points and carry the same caveat.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Measuring with an ohmmeter across the terminals — an ohmmeter injects its own current into a live source and reads nonsense. Internal resistance can only be inferred from how the terminal voltage responds to load.
- Using too light a load — a sag of a millivolt or two is mostly meter noise. Load the source until the terminal voltage drops by a few per cent, without shorting it.
- Ignoring lead and connection resistance — on a low-resistance cell the test leads can contribute more than the cell does, and the calculation cannot separate them.
- Comparing a DC load test with an AC tester reading — the two methods measure different things and the AC figure is normally lower. Compare like with like.
- Treating the result as a fixed property — internal resistance changes with state of charge, temperature and age, so a reading is only meaningful with those conditions recorded alongside it.
Related Free Tools From Arb Digital
For the underlying circuit arithmetic, use the Ohm's law calculator and the electrical power calculator. On the battery side, the battery capacity calculator sizes packs by energy and cell arrangement and the battery life calculator estimates runtime at a given current draw. A source with internal resistance feeding a load is the same topology as a voltage divider, and the resistor combination calculator works out the effective load when several resistances sit in series or parallel. The resistance converter rescales milliohms and kilohms. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It is the resistance inside a voltage source itself, modelled as a resistor in series with an ideal EMF. It is why the voltage at the terminals falls as soon as current is drawn, and why a source cannot deliver unlimited current.
No. An ohmmeter works by pushing its own small current through a passive component, and a live source fights that. The only workable approach is a load test: measure the terminal voltage with and without a load and calculate the resistance from the change.
Because the EMF cancels out of the arithmetic. Taking two loaded readings in quick succession removes any error from a source whose open-circuit voltage is drifting, which is common for cells that have recently been charged or discharged.
There is no single answer, because it depends entirely on chemistry, size and construction. What is useful is the trend for one particular cell measured the same way over time: a resistance that has risen substantially from its as-new value indicates ageing.
Maximum power transfer happens when the load resistance equals the internal resistance, and at that point the two dissipate equal amounts. That is fine when the source energy is free and the signal is scarce, and wrong for anything battery powered.
Yes. Internal resistance rises sharply as cells get cold, which is why a battery that cranks an engine easily in warm weather can fail to do so at low temperature even though its stored charge has barely changed.
A terminal voltage at or above the open-circuit reading is impossible for a passive source, so one of the measurements is wrong. Common causes are a stale open-circuit reading taken before the cell recovered, a meter on the wrong range, or a charger still connected.
This tool is provided for educational and measurement use. It models a source as a constant EMF with a single constant series resistance and cannot separate cell resistance from lead and connection resistance; it publishes no cell or circuit-protection ratings, and any mains or high-current installation must be signed off by a qualified electrical professional.
