How to Calculate the Resistance of a Variable Resistor

Use this interactive calculator to estimate the resistance between a potentiometer terminal and its wiper, the remaining resistance to the opposite terminal, and the no-load output voltage if the component is used as a voltage divider. It supports linear and audio-style tapers so you can model practical variable resistors more realistically.

Total resistance

Resistance unit

Wiper position (%)

Taper type

Supply voltage across the full resistor (optional)

Enter the variable resistor values and click Calculate resistance to view the segment resistances and chart.

Expert guide: how to calculate the resistance of a variable resistor

A variable resistor is a component whose resistance can be adjusted by rotating a shaft, sliding a control, or turning a trim screw. In practice, the term often refers to a potentiometer when all three terminals are used, or a rheostat when only two terminals are used. Understanding how to calculate the resistance of a variable resistor is essential in electronics because the setting of the wiper directly affects current, voltage division, signal level, timing networks, and calibration accuracy.

The core idea is simple: a variable resistor has a fixed total resistance from end to end, and the movable wiper splits that total into two partial resistances. If the element is linear, the resistance changes in direct proportion to position. If the element is audio or logarithmic, the resistance changes according to a nonlinear curve designed to better match human hearing or control behavior.

What a variable resistor actually contains

Most variable resistors contain a resistive track with two end terminals and one moving wiper. If you call the terminals A and B, and the wiper W, then the total resistance is:

R_AB = total rated resistance

When the wiper moves, it divides that track into:

R_AW: resistance from terminal A to the wiper
R_WB: resistance from the wiper to terminal B

Ignoring small contact resistance, the two sections always add up to the full nominal resistance:

R_AW + R_WB = R_AB

The basic formula for a linear variable resistor

If the taper is linear, the resistance changes proportionally with mechanical position. Let the wiper position from terminal A be p, where 0 means fully at A and 1 means fully at B. Then:

R_AW = R_AB × p
R_WB = R_AB × (1 – p)

If your position is in percent rather than decimal, convert it first:

p = position % / 100

Example: suppose you have a 10 kΩ linear potentiometer set to 30% from terminal A. Then:

R_AW = 10,000 × 0.30 = 3,000 Ω
R_WB = 10,000 × 0.70 = 7,000 Ω

This is the most direct answer to the question of how to calculate the resistance of a variable resistor when the part is linear and unloaded.

How to calculate resistance when used as a rheostat

A rheostat is simply a variable resistor used with two terminals instead of three. Usually one end terminal and the wiper are connected into the circuit. In that case, the effective resistance is just the resistance between those two chosen points. If you use terminal A and the wiper, then the adjustable resistance is R_AW. If you use terminal B and the wiper, the adjustable resistance is R_WB.

Read the total resistance value from the component marking or data sheet.
Identify which end terminal is being used with the wiper.
Measure or estimate the wiper position.
Apply the linear or nonlinear taper formula.

For reliable rheostat operation, many designers tie the wiper to the same end terminal used in the circuit. That way, if the wiper momentarily loses contact, the resistance does not jump to infinity.

Calculating a variable resistor in a voltage divider

When all three terminals are used, the component becomes a potentiometer and acts as a voltage divider. If a supply voltage V_in is connected across A and B, and the output is measured at the wiper relative to terminal A, then under no-load conditions the output voltage is:

V_out = V_in × R_AW / R_AB

For a linear taper, this simplifies to:

V_out = V_in × p

Example: a 5 V supply is applied across a 10 kΩ linear potentiometer. At 60% position:

R_AW = 10,000 × 0.60 = 6,000 Ω
R_WB = 4,000 Ω
V_out = 5 × 0.60 = 3.0 V

Why taper matters so much

Not every variable resistor is linear. Audio controls commonly use logarithmic or audio taper tracks because human hearing responds approximately logarithmically to sound intensity. At the mechanical midpoint, an audio taper control often produces only a small fraction of the total resistance on one side, not 50%. That is why a volume knob can feel natural instead of becoming too loud too quickly.

For idealized calculation, a simple approximation can be used. One common model assumes the midpoint corresponds to roughly 10% of total resistance on one side. That is the approximation used by many quick calculators because it represents common audio behavior better than a straight line.

Series or taper reference	Statistic	Why it matters in calculation
E12 preferred resistor series	12 standard values per decade, commonly associated with 10% tolerance	Helpful when choosing nearby fixed resistor replacements or checking whether a measured variable setting matches a standard value.
E24 preferred resistor series	24 standard values per decade, commonly associated with 5% tolerance	Useful for finer resistance selection in calibration and divider design.
Linear potentiometer midpoint	50% travel gives about 50% of total resistance	Direct proportional calculation.
Audio taper midpoint	Often near 10% to 20% of total resistance on one side, depending on design	Mechanical midpoint does not equal electrical midpoint, so simple half-and-half assumptions are wrong.

Step by step method for manual calculation

Identify the total resistance. Common values include 1 kΩ, 5 kΩ, 10 kΩ, 50 kΩ, 100 kΩ, and 1 MΩ.
Determine the type. Is it linear, audio, reverse audio, wirewound, or trimmer?
Define the reference direction. Decide whether position is measured from terminal A toward terminal B.
Convert the position to a decimal. Example: 72% becomes 0.72.
Calculate the partial resistances. Use proportional formulas for linear parts or an approved taper approximation for audio types.
If voltage is applied, compute divider output. Use the voltage divider equation if the output is unloaded or lightly loaded.
Check tolerance and loading. Real parts are not perfect, and external circuits can shift the effective output.

Worked examples

Example 1: linear 50 kΩ potentiometer at 25%

Total resistance: 50,000 Ω
Position: 0.25
R_AW = 50,000 × 0.25 = 12,500 Ω
R_WB = 50,000 × 0.75 = 37,500 Ω

Example 2: 100 kΩ audio taper control near midpoint

If a quick audio taper model puts the midpoint at about 10% of total resistance on the lower side, then at 50% travel:

R_AW ≈ 10,000 Ω
R_WB ≈ 90,000 Ω

This explains why audio controls do not follow the same electrical split as linear controls.

Example 3: rheostat used for current control

Suppose a 25 Ω wirewound variable resistor is used between one end terminal and the wiper, and the wiper is positioned at 80% from the chosen end. The effective series resistance is:

R = 25 × 0.80 = 20 Ω

If a 12 V source drives a purely resistive load in series with that rheostat, Ohm’s law can then be applied to estimate current.

Real-world factors that affect the calculated value

Theoretical calculations are straightforward, but practical electronics introduce several factors that change measured behavior:

Tolerance: a part labeled 10 kΩ may actually measure 9 kΩ, 10.5 kΩ, or another value within its tolerance band.
Contact resistance: the wiper introduces a small extra resistance, especially at low-ohm settings.
Loading: if the wiper output is connected to a low-impedance circuit, the divider equation changes because the lower or upper leg is effectively shunted.
Temperature coefficient: resistance can change with temperature.
End resistance: many potentiometers do not go perfectly to 0 Ω at the mechanical end stop.
Power rating: a variable resistor may overheat if too much current flows through it.

Variable resistor type	Representative total resistance range	Typical use	Calculation note
Carbon film panel potentiometer	1 kΩ to 1 MΩ	Volume, tone, user control knobs	Often linear or audio taper; check midpoint behavior before assuming 50% split.
Cermet trimmer potentiometer	100 Ω to 2 MΩ	Calibration and fine adjustment	Excellent for precise setpoints, but still subject to tolerance and wiper contact effects.
Wirewound rheostat	1 Ω to 10 kΩ	Current limiting, power control	Often preferred at higher power; resistance may change in discrete steps because of winding turns.
Digital potentiometer	1 kΩ to 1 MΩ	Microcontroller controlled adjustment	Resistance changes in finite steps set by code, not continuous motion.

How to measure a variable resistor with a multimeter

Disconnect power from the circuit.
Measure between the two outer terminals to verify the total resistance.
Measure between one outer terminal and the wiper.
Rotate the shaft or move the slider and watch the reading change.
Measure from the wiper to the other outer terminal.
Confirm that the two partial resistances add up to the total resistance, approximately.

This direct test is often the best way to verify whether a control is linear, audio taper, worn out, or electrically noisy.

Common mistakes people make

Assuming every potentiometer is linear.
Forgetting to convert percent to decimal.
Using the wrong reference end terminal.
Ignoring the effect of a load connected to the wiper.
Mixing kΩ and Ω units during calculation.
Overlooking tolerance and expecting exact measured values.

When the simple formulas are sufficient

If your variable resistor is linear, the circuit connected to the wiper has very high input impedance, and the total resistance is within tolerance, the simple formulas are usually all you need. That covers many educational, hobby, and basic design calculations. The calculator above is ideal for this scenario because it instantly gives both segment resistances and a visual chart of how they vary across travel.

Authoritative references for further study

If you want to go deeper into resistance, Ohm’s law, and divider behavior, the following sources are useful:

Final takeaway

To calculate the resistance of a variable resistor, start with the total end-to-end resistance, identify the wiper position, and then split the total according to the taper. For a linear control, the relationship is directly proportional. For audio taper, the relationship is intentionally nonlinear, so midpoint travel does not produce midpoint resistance. If the component is used as a potentiometer, you can also calculate the output voltage with the voltage divider formula. Once you understand those few relationships, variable resistor calculations become fast, reliable, and easy to apply in real circuits.

How To Calculate The Resistance Of A Variable Resistor