Dipole Antenna Radiation Resistance Calculator
Find the radiation resistance of a dipole antenna from its length and operating frequency using the short-dipole approximation, with an accuracy note near the half-wave case.
📶 What is Dipole Antenna Radiation Resistance?
Radiation resistance is the equivalent resistance that would dissipate power at exactly the rate a dipole antenna actually radiates it into space, given the same feed current. It is not a physical resistive loss, no heat is generated, but expressing radiated power this way lets engineers treat an antenna's radiating behavior with the same simple circuit math used for an ordinary resistor.
RF and antenna engineers estimate radiation resistance constantly when designing compact antennas and matching networks. An amateur radio operator building a shortened HF dipole for a limited space estimates its radiation resistance to size an appropriate matching network, since a low radiation resistance means small losses elsewhere in the system can waste a large fraction of transmitted power. An antenna designer sanity-checks a simulation result against the short-dipole approximation for a quick order-of-magnitude confirmation before trusting a more complex electromagnetic model. A student learning antenna theory uses the well-documented half-wave dipole case (73 ohms) as a reference point to understand where the simple short-dipole formula starts to break down.
A common misconception is that this approximation applies accurately at any dipole length. In reality, the short-dipole formula assumes a triangular current distribution that only holds well for electrically short antennas, well below half a wavelength. As L/lambda approaches 0.5, the true current distribution becomes sinusoidal rather than triangular, and the formula's accuracy degrades, most visibly at the classic half-wave dipole case, where the true radiation resistance (about 73 ohms) is noticeably higher than the roughly 49.3 ohms the short-dipole formula predicts at that same length.
This calculator takes a dipole's physical length and operating frequency, and returns the radiation resistance using the short-dipole approximation, along with the wavelength, the L/lambda ratio, an explicit accuracy note as that ratio approaches or exceeds 0.5, and a chart showing how radiation resistance changes across the formula's intended 0 to 0.5 range.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Electrically Short HF Dipole
L = 1 m, f = 30 MHz
Example 2 — Moderate-Length VHF Dipole
L = 1.4 m, f = 100 MHz
Example 3 — Half-Wave Boundary Case
L = 1.5 m, f = 100 MHz (L/λ = 0.5 exactly)
❓ Frequently Asked Questions
🔗 Related Calculators
What is radiation resistance of a dipole antenna?
Radiation resistance is the equivalent resistance that, if it dissipated power at the same rate the antenna actually radiates it, would draw the same current as the real antenna. It is not a physical resistive loss but a convenient way to express how effectively an antenna converts input current into radiated electromagnetic power, expressed in ohms just like an ordinary resistor.
How do you calculate the radiation resistance of a short dipole?
Rr = 20 times pi squared times (L divided by lambda) squared, where L is the dipole's physical length and lambda is the wavelength, found from lambda = speed of light divided by frequency. This short-dipole approximation assumes a roughly triangular current distribution and is most accurate for L/lambda well below 0.5.
Why is the short-dipole formula only an approximation?
It assumes the antenna current tapers linearly (triangularly) from maximum at the feed point to zero at each end, which is a good model only for an electrically short dipole. As the dipole length approaches half a wavelength, the true current distribution becomes closer to a sinusoidal shape, and the short-dipole formula increasingly underestimates the actual radiation resistance.
What is the radiation resistance of a half-wave dipole?
The exact radiation resistance of a half-wave dipole (L/lambda = 0.5), derived from the sine and cosine integral solution to the antenna's true sinusoidal current distribution, is approximately 73 ohms. The short-dipole approximation used on this page gives only about 49.3 ohms at that same length, a real and well-documented discrepancy, not a calculation error.
How accurate is this calculator near L/lambda = 0.5?
Accuracy degrades noticeably as L/lambda approaches 0.5. This calculator shows an explicit note once L/lambda exceeds about 0.3, and treats the formula's output as unreliable for reference purposes once L/lambda exceeds 0.5, well outside the short-dipole approximation's intended range.
Why does radiation resistance increase with frequency for a fixed physical length?
Increasing frequency shortens the wavelength lambda, which raises the L/lambda ratio for a fixed physical length L, and radiation resistance scales with the square of that ratio. This is why a physically short antenna radiates much more efficiently at higher frequencies (electrically longer relative to its wavelength) than at lower ones.
Is radiation resistance the same as antenna impedance?
No. Radiation resistance is only the resistive part of an antenna's feed-point impedance that corresponds to radiated power. The full feed-point impedance also includes reactance (nonzero unless the antenna is exactly resonant) and, for a real conductor, a small additional resistance from ohmic (heat) losses, both left out of this calculator's radiation-only result.
What units does this calculator expect for frequency?
Enter frequency in megahertz (MHz). The calculator converts it internally to hertz (multiplying by 1,000,000) before computing wavelength as the speed of light divided by frequency, so results come out correctly in meters and ohms without any manual unit conversion needed.
Why does a short antenna have low radiation resistance and why does that matter?
A physically short dipole has a small L/lambda ratio, and since radiation resistance scales with the square of that ratio, it can be just a few ohms or less. A low radiation resistance matters because it becomes comparable to, or smaller than, the antenna's unavoidable ohmic loss resistance, so a larger fraction of input power is wasted as heat instead of radiated, a key design challenge for compact antennas.
Can this formula be used for a monopole (quarter-wave whip) antenna instead of a dipole?
Not directly. A quarter-wave monopole over a good ground plane behaves like half of a half-wave dipole and has a radiation resistance of about 36.5 ohms at resonance, roughly half the dipole's 73 ohms, because the ground plane reflects the missing half of the antenna. This calculator's short-dipole formula is specifically for a two-sided dipole, not a grounded monopole.