Every resistor generates a small random voltage across its own terminals simply because it is above absolute zero. The charge carriers inside it are in thermal motion, and that motion produces a fluctuating potential with no input signal and no external cause. This is Johnson–Nyquist noise, and it sets the floor below which no circuit design can push a resistive source. The resistor noise calculator above gives you that floor for a specific resistance, temperature and bandwidth.
Arb Digital publishes free engineering calculators that state their assumptions instead of hiding them. The number here is a theoretical floor derived from a physical law, not a measurement of your circuit. A real resistor will always be noisier, because it also contributes excess low-frequency noise and because whatever amplifier follows it adds its own. What this page gives you is the best you could possibly do — the reference point you need when a measurement comes back disappointing.
What This Resistor Noise Calculator Does
It computes four quantities from the same relationship. The hero figure is the RMS open-circuit noise voltage across the resistor over your stated bandwidth. The grid gives the voltage spectral density in nanovolts per root hertz, the bandwidth-independent way engineers quote resistor noise; the RMS short-circuit noise current, which matters when the resistor feeds a transimpedance stage; the available noise power into a matched load; and a peak-to-peak estimate for reconciling a calculation with an oscilloscope trace.
The available noise power surprises people most: it does not depend on resistance at all. A 50 Ω termination and a 1 MΩ input resistor offer the same available noise power at the same temperature and bandwidth, because the larger resistor's higher voltage is exactly cancelled by its worse ability to drive a matched load. That is why the matched noise floor of a radio system is one number in dBm rather than something you look up per component.
How to Use It
- Enter the resistance the noise actually comes from. In a divider or feedback network the noise-generating resistance at a node is usually a parallel combination. Work it out with the resistor combination calculator first.
- Pick a temperature convention and say which one you picked. The default 290 K is the reference used throughout noise figure work; 300 K or 293 K is more honest for a bench measurement. Switch the selector to Celsius if you are working from an ambient reading.
- Enter a real noise bandwidth, not the −3 dB bandwidth. A single-pole filter passes noise over π/2 times its −3 dB corner, about 57 per cent more than you would guess. Sharper filters get closer to their nominal corner.
- Read the density, not just the total. The nV/√Hz figure is what you compare against an amplifier datasheet.
- Treat the peak-to-peak number as a convention. Gaussian noise has unbounded peaks; watch long enough and you will beat any factor.
The Formula: How Thermal Noise Is Calculated
The Johnson–Nyquist relation gives the mean-square open-circuit noise voltage of a resistance R at absolute temperature T over noise bandwidth B as Vn² = 4kTRB, so Vn = √(4kTRB). Here k is the Boltzmann constant, fixed exactly since the 2019 SI redefinition at 1.380649 × 10−23 joules per kelvin in the NIST CODATA tables. The corresponding short-circuit noise current follows directly from Ohm's law: In = Vn/R = √(4kTB/R).
Divide out the bandwidth and you get the spectral density, en = √(4kTR), quoted in volts per root hertz. The available noise power — the power delivered into a conjugately matched load — is P = kTB, with the resistance gone entirely. Expressed in dBm this becomes 10 log10(kTB/1 mW), which at 290 K and a one-hertz bandwidth is the familiar −174 dBm/Hz that every radio link budget starts from.
Work the defaults by hand. With R = 1 kΩ and T = 290 K, 4kTR = 1.6016 × 10−17, whose square root is 4.00 × 10−9 — so 4.00 nV/√Hz, the textbook value for a kilohm at T0. Over 10 kHz, multiply by √10000 = 100 for 400 nV RMS, and the noise current is 400 nV ÷ 1 kΩ = 0.400 nA. The available power is kTB = 4.00 × 10−17 W, or −134.0 dBm — consistent with −174 dBm/Hz plus 40 dB.
Why the Temperature Convention Matters More Than It Looks
Noise voltage goes as the square root of absolute temperature, so the gap between 290 K and 300 K is tiny: about 1.7 per cent in voltage, under 0.15 dB in power. No measurement is upset by that. What gets upset is the comparison between two published figures, because the conventions belong to different traditions and mixing them silently makes correct numbers look inconsistent.
The 290 K figure is a definition, not an observation. It was adopted as the reference temperature T0 for noise factor precisely so that noise figure could be a property of a device rather than of the room it was measured in, and every low-noise amplifier datasheet refers to it. The 300 K figure is a rounded stand-in for room temperature used in teaching and analogue design. Neither is wrong. Reporting a noise figure computed from a 300 K floor as though it referred to T0 is wrong.
The temperature also has to be that of the resistor, not the room. A part dissipating half a watt in a small package can sit fifty degrees above ambient. If it is running warm, get its body temperature from the derating method on the resistor power rating calculator and use that figure here.
This Is a Floor, Not a Measurement
The single most important limitation of this page is that thermal noise is a lower bound. Three things routinely make a real circuit noisier, and none of them appear in the formula.
The first is excess noise, also called current noise or 1/f noise, which only exists when current flows and depends heavily on construction. Carbon composition parts are worst by a wide margin, thick film intermediate, thin film and bulk metal foil close to thermal-noise-limited. It rises as frequency falls, so at audio and DC-precision frequencies it can dominate entirely.
The second is the amplifier that follows. Every gain stage adds its own voltage noise and current noise, and that current noise flowing in your source resistance produces additional voltage. Every amplifier has an optimum source resistance, and going above it degrades quickly.
The third is everything that is not noise at all: mains hum, supply ripple, ground loops and radiated pickup. If your measured floor is an order of magnitude above the figure here, the cause is almost never thermal physics. NIST's work on Johnson noise thermometry shows what it takes to measure thermal noise accurately enough to serve as a primary thermometer, which is a useful calibration for how easily a bench measurement goes wrong.
Noise Bandwidth Is Not the Same as −3 dB Bandwidth
The B in the formula is the equivalent noise bandwidth: the width of an ideal brick-wall filter passing the same total noise power as your real one. Real filters roll off gradually and keep passing noise past their corner, so it is always larger than the −3 dB figure.
For a single-pole RC filter the ratio is π/2, about 1.571, so a 1 kHz corner passes noise as though it were 1,571 Hz wide — nearly two decibels of extra noise power that a naive calculation misses. A two-pole Butterworth is about 1.11 times its corner, a three-pole about 1.05, and higher orders converge on 1. The other half of the question is your instrument: a scope's displayed noise depends on its own analogue bandwidth limit, not on your circuit, so turning a 500 MHz scope down to 20 MHz cuts displayed noise by a factor of five before anything has changed.
How This Sits Next to the Other Noise Tools
This page gives the thermal noise generated by a passive resistance. It is the input to a noise figure calculation, not a substitute for one: the noise figure calculator handles how much a device degrades a signal-to-noise ratio relative to that 290 K floor and cascades stages with the Friis relation.
The decibel calculator turns ratios into decibels and the dBm to watts converter moves between radio's absolute power scale and plain watts. The op-amp gain calculator sets the gain this noise gets multiplied by. For signal amplitudes rather than noise, the RMS voltage calculator converts between RMS, peak and peak-to-peak for deterministic waveforms — a different job, because a sine wave has a fixed crest factor and Gaussian noise does not. And the noise exposure calculator is occupational sound pressure: nothing on this page concerns sound.
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
- Quoting a noise voltage without a bandwidth — give the density in nV/√Hz or state the bandwidth alongside the total.
- Using the −3 dB corner as the noise bandwidth — for a single-pole filter that understates the noise by 57 per cent in power, and the error is silent.
- Mixing 290 K and 300 K conventions between sources — small in absolute terms, but it makes two correct figures look like they disagree.
- Using the largest resistor in the schematic — the noise-generating resistance at a node is usually the parallel combination, which can be far smaller.
- Treating this floor as a prediction of measured noise — excess resistor noise, amplifier noise and pickup all sit on top of it, and one of them usually dominates.
Related Free Tools From Arb Digital
Get the equivalent source resistance from the resistor combination calculator and check the part is not running hot with the resistor power rating calculator. From the answer, the decibel calculator and dBm to watts converter handle the conversions and the noise figure calculator takes it into a receiver chain. For signal-side work, the RMS voltage calculator and op-amp gain calculator cover waveform conversion and stage gain. Everything sits on the free online tools hub.
Frequently Asked Questions
It is the random voltage a resistance generates across itself purely because it is above absolute zero. Its mean-square value is 4kTRB, where k is the Boltzmann constant, T the absolute temperature, R the resistance and B the noise bandwidth. It is a consequence of thermodynamics rather than a defect in the component.
Use 290 K if the result feeds any noise figure or noise factor work, because 290 K is the standard reference temperature those definitions are built on. Use 300 K or 293 K if you are describing an actual room-temperature bench measurement. The difference is about 1.7 per cent in voltage and 0.15 dB in power, so the number barely changes, but stating which convention you used stops two correct figures looking inconsistent.
Thermal noise has a flat power spectral density across any bandwidth a circuit cares about, so total noise power is proportional to the bandwidth you accept. Because voltage goes as the square root of power, RMS noise voltage grows with the square root of bandwidth.
No. The available noise power into a matched load is kTB and does not contain the resistance at all. A large resistor produces a larger open-circuit noise voltage but is correspondingly worse at driving current into a matched load, and the two effects cancel exactly. This is why the matched noise floor of a radio system is a single figure of about minus 174 dBm per hertz at 290 K regardless of the impedance chosen.
No, it is the theoretical floor. A real resistor also produces excess noise that depends on its construction and on the current through it, the amplifier after it adds its own voltage and current noise, and mains hum, supply ripple and radiated pickup usually sit above both. Treat the figure on this page as the best case that no circuit design can beat, and as a reference for judging how far above the floor a real measurement sits.
Noise bandwidth is the width of an ideal brick-wall filter that would pass the same total noise power as your real filter. Real filters keep passing noise beyond their corner frequency, so it is always the larger number. A single-pole RC filter has a noise bandwidth of pi over two times its corner, about 1.571 times, while a two-pole Butterworth is about 1.11 times and higher orders approach 1.
Gaussian noise has no true peak value, so any peak-to-peak figure is a stated convention rather than a measurement. The default factor of 6.6 corresponds to a window of plus and minus 3.3 standard deviations, which the noise exceeds roughly 0.1 per cent of the time. Some engineers use 6 and some use 8. Observe for long enough and you will always see a larger excursion than the factor predicts.
Thermal noise itself depends only on resistance and temperature, so a carbon composition resistor and a metal foil resistor of the same value at the same temperature generate identical thermal noise. What differs sharply is excess noise, which only appears when current flows and which is far worse in carbon composition parts than in thin film or bulk metal foil. That excess contribution is not modelled here.
This tool is provided for educational and preliminary design use. It computes the theoretical Johnson-Nyquist thermal noise floor of an ideal resistance and does not model excess or 1/f noise, amplifier noise, shot noise, interference or pickup. Real measured noise will be higher. Verify any design against measurement.
