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Voltmeter Loading Error

When you connect a voltmeter across a circuit, its finite input resistance draws some current and changes the voltage being measured. This formula gives the actual measured voltage, which is lower than the true voltage if the source resistance is significant. To minimise error, the voltmeter should have a very high input resistance compared to the circuit resistance. It is a practical consideration in precision measurements.

Written by the Vorzep Team

Instrumentation Measurement Error

Voltmeter Loading Error Calculator

How much a meter's finite input resistance pulls down the voltage it is trying to measure.

Vm = Vt · Rm / (Rm + Rs)
RsRm

Inputs

Drag the handle (or use arrow keys on it) to reorder
Tolerance and AC options
Calculating loading error…

Results

Loading error
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Formula breakdown

Reading accuracy versus meter resistance

The curve shows what percentage of the true voltage the meter displays. The shaded band is the reading range allowed by your loading-error limit.

Equivalent circuit

Conversion tables

%
Rm/RsLoading errorReading for Vt = 10 V
Target errorMin Rm/RsMin Rm for Rs = 10 kΩ

Typical meter input resistances

InstrumentInput resistance

Key formulas and references

Vm = Vt · Rm / (Rm + Rs)
Loading error = Rs / (Rm + Rs) × 100 % ≈ Rs/Rm × 100 %
Divider: Rs = R1‖R2, Vt = Vs · R2 / (R1 + R2)
Analogue meter: Rm = sensitivity (Ω/V) × range (V)
Rm,min = Rs · (100 − e) / e
Correction: Vt = Vm · (Rm + Rs) / Rm
f−3dB = 1 / (2π · (Rs‖Rm) · Cm)
  1. Horowitz & Hill, The Art of Electronics, Cambridge University Press: source and load impedance.
  2. Nilsson & Riedel, Electric Circuits, Pearson: Thévenin equivalent circuits.
  3. Wolf & Smith, Student Reference Manual for Electronic Instrumentation Laboratories, Prentice Hall: meter loading.
  4. Morris & Langari, Measurement and Instrumentation, Academic Press.
  5. Tektronix, The XYZs of Oscilloscopes primer: probe and input loading.

Variables

Symbol Quantity Unit
V_measured Measured voltage (with loading effect) V
V_true True (open-circuit) voltage V
R_m Voltmeter internal resistance Ω
R_s Source (Thevenin) resistance Ω

What it means

When a voltmeter is connected to measure a voltage, it draws current from the circuit, affecting the measured value. The loading error is due to the meter’s internal resistance R_m forming a voltage divider with the source resistance R_s. The measured voltage is V_measured = V_true · (R_m / (R_m + R_s)). To minimize loading error, the voltmeter should have a very high resistance compared to the source resistance. This is why digital voltmeters have input impedances of 10MΩ or more. Example: A source with V_true=10V and R_s=100kΩ. A voltmeter with R_m=1MΩ reads V_measured = 10 * (1e6/(1e6+1e5)) = 10 * (1e6/1.1e6) = 9.09V, giving a 9.1% error. A meter with 10MΩ would give 9.9V (1% error).

Worked example

Voltmeter Loading Error – Practical Example

Real‑World
Scenario: A true voltage of 5 V appears across a 1 MΩ source. A voltmeter with 1 MΩ input resistance measures it. Find the measured voltage.
ParameterValue
Vtrue5 V
Rs1 MΩ
Rm1 MΩ
FormulaVm = Vtrue · Rm/(Rm+Rs)
1Rm/(Rm+Rs) = 1/(1+1) = 0.5
2Vm = 5 × 0.5 = 2.5 V
Final Design Vm = 2.5 V ✓ Loading error
Why: Voltmeter loading causes measurement error – choose a meter with much higher resistance than the source.

Common mistakes

Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.

Applications

Voltmeter loading error occurs because the meter draws current, forming a voltage divider with the source resistance. V_measured = V_true · (R_m/(R_m+R_s)). Engineers use this to understand why high‑impedance voltmeters are needed for low‑power circuits. By selecting a meter with high input impedance, they minimise this error. This is a practical consideration in circuit measurements.

  • Measurement error analysis in voltage measurements
  • Selection of voltmeters with adequate input impedance
  • Design of buffer amplifiers for measurement isolation
  • Educational understanding of loading effects

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  • Published July 10, 2026
  • Last updated August 12, 2026