Internal resistance calculator
A 12 V battery that reads 11 V while delivering 2 A has an internal resistance of 0.5 Ω, with 1 V lost inside the cell. Enter the open-circuit voltage, the loaded voltage and the current to check a battery or a lab result. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Emf
- 12
- Terminal voltage
- 11
- Load current
- 2
- Voltage drop
- 1 ohm
- Internal resistance
- 0.5
This battery internal resistance calculator returns the ohmic internal resistance of a cell from its electromotive force, the terminal voltage measured under load, and the load current, using the linear identity r equals open-circuit EMF minus terminal voltage, all divided by load current. The open-circuit EMF is the voltage you would measure with no load attached. Under load a real cell drops voltage across its internal resistance, so the usable terminal voltage is lower than the EMF for a discharging current. Rearranging V equals ε minus I times r isolates the unknown r in one division. Classic checks include a twelve-volt cell that reads eleven volts while delivering two amperes, which has half an ohm of internal resistance, and a 1.5-volt dry cell that sags to 1.2 volts at half an ampere, which has 0.6 ohms. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Where internal-resistance checks fit in study, design, and software
Students meet r equals (ε minus V) over I when a circuit unit introduces real batteries, when a lab asks why a fresh cell reads lower under load than on open circuit, or when a contest problem gives EMF, terminal voltage, and current and asks for internal resistance without a SPICE run. Teachers can pre-generate answer keys for modest EMFs and currents without trusting opaque calculator apps that silently mix millivolts with volts or switch between peak and RMS without saying so.
Developers call the same contract from scripts to seed deterministic test vectors for battery UIs, to normalize user-entered cell parameters before a power-budget sketch, or to satisfy programming-challenge statements that demand internal resistance in ohms rather than a hand-waved estimate. Field technicians and makers use it for quick checks on twelve-volt and nine-volt rails, starter-motor loads, and simple DC supplies when only a measured open-circuit voltage, a loaded terminal voltage, and a clamp-meter current are available.
What you can do with it
Homework and lab checks
Compute internal resistance from EMF, loaded terminal voltage, and load current before grading battery worksheets or DC lab write-ups.
Design and maker checks
Estimate cell internal resistance from a measured open-circuit voltage, a loaded rail voltage, and a clamp-meter current.
FAQ
What does the internal resistance calculator cost?
It is free in your browser on this page.
Which formula does it use?
r = (ε − V) / I, where ε is the open-circuit electromotive force, V is loaded terminal voltage, and I is load current. It also returns the internal drop ε − V.
What if the load current is zero?
Internal resistance r = (ε − V) / I is undefined when no current flows, which is the open-circuit case.
What units should I use?
Use a consistent set such as volts, volts, and amperes. Then internal resistance is in ohms. The tool does not convert prefixes for you.
How is this different from an EMF terminal-voltage calculator?
That tool solves V = ε − I r when r is already known. This page solves the inverse: given ε, V, and I, it returns r in ohms.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/internal-resistance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"emf":12,"terminal_voltage":11,"load_current":2}'const res = await fetch("https://api.kit.forhosting.com/phys/internal-resistance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"emf": 12,
"terminal_voltage": 11,
"load_current": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/internal-resistance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"emf": 12,
"terminal_voltage": 11,
"load_current": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/internal-resistance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"emf":12,"terminal_voltage":11,"load_current":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"emf":12,"terminal_voltage":11,"load_current":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/internal-resistance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"emf": 12,
"terminal_voltage": 11,
"load_current": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.internal_resistance",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_value | 1000000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
A load current of zero is rejected with invalid_input because r is undefined when no current flows.
What internal resistance is and what the response contains
Internal resistance is the effective ohmic resistance that lives inside a battery or electrochemical cell, modelled as a single resistor in series with an ideal electromotive-force source. When a load draws current I in the discharge direction, Ohm's law on that internal resistance produces a voltage drop equal to I times r, so the voltage left at the external terminals is V equals ε minus I times r. Negative current is allowed algebraically and models a charging direction if you keep a consistent sign convention; a negative computed r means the stated terminal voltage sits on the opposite side of the EMF from the stated current direction. This calculator rearranges that identity and returns r equals (ε minus V) divided by I as internal_resistance, together with voltage_drop equal to ε minus V, which is the potential lost inside the cell. The response also echoes the three inputs emf, terminal_voltage, and load_current after stable rounding, tags the method as r equals (emf minus V) over I, repeats a short formula string, and labels the unit as ohm when the inputs are SI-consistent volts, volts, and amperes. Zero load current is not treated as a convenient open-circuit shortcut: with I equal to zero the terminal voltage equals the EMF and the formula would divide by zero, so the engine rejects the request with invalid_input instead of inventing infinity or a NaN. There is no Peukert capacity model, no temperature-dependent r, no Thevenin multi-source network, and no Monte Carlo sampling: the engine either evaluates the closed form inside the supported numeric range or rejects the input with invalid_input.
How EMF, terminal voltage, and load current are read and how r stays reproducible
Each value must be a finite decimal within the documented magnitude ceiling; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a message that names the field so a bad cell does not become a wrong resistance. Load current must not be zero: a zero I fails immediately because internal resistance r equals (ε minus V) divided by I is undefined when the load current is zero, which is the open-circuit case where terminal voltage already equals the EMF and r is not determined. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals. The preferred field for electromotive force is emf, but aliases E, epsilon, open_circuit_voltage, and voc are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Terminal voltage prefers terminal_voltage, with aliases V, vt, V_t, and voltage. Load current prefers load_current, with aliases I, current, i, amps, and amperes. Missing any of the three required fields fails with invalid_input and a message that names the missing field. Computation uses the closed forms voltage_drop equals emf minus terminal_voltage and internal_resistance equals voltage_drop divided by load_current, then rounds to twelve decimal places for JSON goldens and collapses negative zero for clean comparisons. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline.
Where internal-resistance checks fit in study, design, and software
Product and education tools use the endpoint when a learner types EMF, terminal voltage, and load current and the UI must show both the internal drop and the resistance. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with electrical power or resistor helpers when you need related circuit steps, and with other physics endpoints when you are building a small lab of free, deterministic electrical calculators for study and software tests.
Integration use cases
Deterministic test fixtures
Generate reproducible r and voltage-drop values for unit tests, battery demos, and CI assertions on r = (ε − V) / I.