An Antenna Radiation Pattern Calculator helps you understand how an antenna radiates energy in different directions. Instead of treating radiation as equal in every direction, the calculator evaluates the relative field strength and radiated power at a selected elevation angle.

This calculator supports three ideal antenna patterns: isotropic radiator, half-wave dipole, and quarter-wave monopole over an ideal ground plane. You can enter an elevation angle from the horizon and calculate the normalized field strength, relative radiated power, power percentage, and attenuation from the pattern maximum in decibels (dB).

The calculator is designed for ideal antenna-pattern analysis. It does not attempt to predict the exact radiation pattern of a physically installed antenna because real installations are affected by factors such as the ground plane, nearby objects, antenna mounting, terrain, and other electromagnetic interactions.

What Is an Antenna Radiation Pattern?

An antenna radiation pattern describes how the radiation from an antenna varies with direction. Some antennas radiate relatively strongly in particular directions and weakly in others. Understanding this directional behavior is fundamental to antenna design, RF engineering, wireless communications, and radio systems.

A radiation pattern can be represented using either field strength or radiated power.

The field pattern describes the relative amplitude of the electromagnetic field. A normalized field pattern typically assigns a value of 1 to the maximum field strength.

The power pattern is related to the square of the field magnitude:

P_relative = ∣F∣²

where:

• F = normalized field strength
• P_relative = relative radiated power

For example, if normalized field strength is 0.5, the corresponding relative power is:

0.5² = 0.25

So a field strength that is 50% of the maximum corresponds to 25% of the maximum relative power.

Radiation patterns are frequently expressed in normalized form because this makes it easier to compare the directional behavior of different antennas without requiring absolute transmitter power or field-strength measurements.

What Does the Antenna Radiation Pattern Calculator Calculate?

This calculator evaluates the ideal radiation behavior of a selected antenna pattern at a specified elevation angle from the horizon.

It provides the following results:

• Ideal Antenna Pattern
• Elevation Angle
• Normalized Field Strength
• Relative Radiated Power (Ratio)
• Relative Radiated Power (%)
• Attenuation from Pattern Maximum (dB)
• Pattern Reference
• Model Limitation

The calculator supports:

1. Isotropic Radiator
2. Half-Wave Dipole
3. Quarter-Wave Monopole

The elevation angle can range from 0° to 90°.

The output is relative rather than absolute. In other words, the calculator does not tell you how many watts an antenna radiates in a particular direction. Instead, it tells you how strong that direction is relative to the maximum of the selected ideal pattern.

How This Antenna Radiation Pattern Calculator Works

The calculation involves several steps.

Step 1: Select an Antenna Pattern

The calculator first asks you to select one of three idealized antenna patterns:

• Isotropic radiator
• Half-wave dipole
• Quarter-wave monopole

The selected pattern determines how the field strength changes with direction.

The isotropic model is particularly simple because it assumes equal radiation in every direction.

The dipole and monopole models use an idealized directional field relationship.

Step 2: Enter the Elevation Angle

The calculator uses an input called:

Elevation Angle from Horizon

The allowed range is:

0 ^∘ ≤ α ≤ 90 ^∘

where α represents the elevation angle.

An elevation of:

• 0° means the direction is along the horizon.
• 30° means the direction is 30° above the horizon.
• 45° means the direction is halfway between the horizon and vertical.
• 90° means the direction is directly overhead.

However, the radiation-pattern formula used for the dipole and monopole models is expressed using an angle measured from the antenna element axis.

Therefore, the calculator converts the elevation angle using:

θ = 90 ^∘ − α

where:

• α = elevation angle from the horizon
• θ = angle from the antenna element axis

For example, an elevation angle of 30° corresponds to:

θ = 90 ^∘ − 30 ^∘ = 60 ^∘

This coordinate conversion is an important part of correctly interpreting the result.

Understanding the Three Antenna Patterns

1. Isotropic Radiator

An isotropic radiator is an ideal theoretical reference that radiates equally in every direction.

It does not have directional lobes or nulls. Its normalized field strength is therefore:

F = 1

regardless of the selected elevation angle.

The relative power is:

P = 1² = 1

or:

100%

The attenuation from the pattern maximum is:

10log₁₀(1) = 0 dB

Therefore, when the isotropic model is selected, the calculator returns the same normalized radiation values at every valid elevation angle.

Why use an isotropic reference?

An isotropic radiator is useful as a theoretical reference when discussing antenna gain and radiation patterns. Real antennas are generally not isotropic, but the ideal reference provides a convenient baseline for describing directional behavior.

It is important not to confuse an isotropic reference with a physically realizable antenna. The isotropic radiator is an ideal mathematical model.

2. Half-Wave Dipole

The half-wave dipole has a directional radiation pattern. Its ideal three-dimensional pattern is commonly visualized as a doughnut surrounding the antenna element.

For the dipole model used by this calculator, the normalized field relationship is:

F(θ) = cos(π2cosθ)sinθ

where θ is the angle from the antenna element axis.

The calculator takes the absolute value of this field expression and normalizes the resulting field so that the pattern maximum is represented by 1.

Dipole at broadside

For a vertical dipole, the broadside direction is horizontal. Therefore, an elevation angle of 0° corresponds to the maximum-radiation direction in the ideal model.

At this direction:

θ = 90 ^∘

and the normalized field reaches its maximum.

Dipole along the element axis

At an elevation angle of 90°:

θ = 0 ^∘

This corresponds to looking along the antenna element.

An ideal half-wave dipole has a radiation null along its element axis, so the calculator sets the pattern field to zero at this boundary.

This is why understanding the difference between elevation angle and element-axis angle is essential when interpreting the calculator.

3. Quarter-Wave Monopole

The calculator also includes a quarter-wave monopole model.

The idealized directional behavior in the modeled hemisphere follows the same mathematical field relationship used for the dipole model.

This provides a useful theoretical approximation for understanding the directional behavior of a vertical quarter-wave monopole.

However, an actual monopole installation may behave differently.

The real radiation pattern can depend on factors including:

• Ground-plane dimensions
• Ground conductivity
• Radial configuration
• Mounting structure
• Nearby conductive objects
• Terrain
• Installation environment

Consequently, the calculator should be treated as an ideal pattern model, rather than a complete electromagnetic simulation of a real monopole installation.

Elevation Angle vs. Antenna Element-Axis Angle

One of the most important concepts in this calculator is the distinction between elevation angle and the angle used by the radiation-pattern formula.

Elevation angle

Elevation is measured upward from the horizon:

• 0° = horizon
• 90° = directly overhead

Element-axis angle

The dipole field formula uses an angle measured from the antenna element axis.

The calculator converts between the two:

θ = 90 ^∘ − α

Consider these examples:

For a vertically oriented antenna, this relationship makes intuitive sense.

A direction along the horizon is perpendicular to the vertical antenna element, while a direction directly overhead is aligned with it.

That is why a vertical dipole has maximum ideal radiation near the horizon and a null along its vertical axis.

How to Use the Antenna Radiation Pattern Calculator

Using the calculator is straightforward.

Step 1: Select the antenna pattern

Choose:

• Isotropic Radiator
• Half-Wave Dipole
• Quarter-Wave Monopole

Step 2: Enter the elevation angle

Enter an angle between:

0 ^∘  and 90 ^∘

Step 3: Calculate the result

The calculator converts the elevation angle into the angle used by the ideal radiation-pattern equation.

Step 4: Review normalized field strength

This shows the field amplitude relative to the pattern maximum.

A value of:

1.000

represents the normalized maximum.

Step 5: Review relative radiated power

The calculator squares the normalized field:

P_relative = F²

Step 6: Review attenuation

The calculator converts relative power into decibels:

A_dB = 10log₁₀(P_relative)

This allows you to understand how much weaker a particular direction is compared with the pattern maximum.

Understanding the Calculator Results

Normalized Field Strength

Normalized field strength represents the field amplitude relative to the maximum of the selected ideal pattern.

The maximum normalized value is:

1

A smaller number indicates weaker field strength in that direction.

This is a relative quantity, not an absolute measurement in volts per meter.

Relative Radiated Power Ratio

The calculator calculates relative power by squaring the normalized field:

P_relative = F²

For example, if:

F = 0.7

then:

P_relative = 0.7² = 0.49

The direction therefore has 0.49 times the power of the normalized pattern maximum.

Relative Radiated Power Percentage

The calculator converts the power ratio to a percentage:

P_% = P_relative × 100

This percentage should be interpreted as relative to the pattern maximum.

It does not mean that a certain percentage of the transmitter's total power is physically radiated in that direction.

For example, a relative power result of 25% means the modeled power density is 25% of the normalized maximum, not that 25% of the transmitter's power is being sent into that direction.

Understanding Radiation Pattern Attenuation in dB

The calculator expresses relative power using:

A_dB = 10log₁₀(P_relative)

Because the input is a power ratio, the 10 log10 relationship is used.

At the pattern maximum:

P_relative = 1

Therefore:

10log₁₀(1) = 0 dB

So 0 dB means the pattern maximum, not zero radiation.

As the relative power decreases, the dB value becomes increasingly negative.

For example, a relative power ratio below 1 produces a negative dB result.

A theoretical radiation null corresponds to zero relative power:

P_relative = 0

Mathematically:

10log₁₀(0)

approaches negative infinity.

The calculator handles this condition by displaying:

Below numerical limit

rather than attempting to display an infinite numerical value.

Field Strength vs. Relative Power

It is important to understand why the calculator squares field strength.

Electromagnetic power is related to the square of field amplitude. Therefore, normalized field and normalized power are not interchangeable.

Suppose the normalized field is:

F = 0.5

The relative power becomes:

P = 0.5²P = 0.25

Therefore:

• Normalized field = 0.5
• Relative power = 0.25
• Relative power percentage = 25%

This distinction is particularly important when interpreting radiation-pattern graphs.

A field pattern and a power pattern may look similar, but their numerical values are different because the power relationship involves the square of the field magnitude.

Practical Antenna Radiation Pattern Examples

Example 1: Isotropic radiator

Select Isotropic Radiator and enter any valid elevation angle.

The ideal model always produces:

• Normalized field = 1
• Relative power = 1
• Relative power = 100%
• Attenuation = 0 dB

This occurs because the isotropic model has no directional variation.

Example 2: Half-wave dipole at broadside

Consider a vertical half-wave dipole and an elevation angle of 0°.

The calculator converts the angle:

90 ^∘ − 0 ^∘ = 90 ^∘

The resulting direction is broadside to the antenna element, where the ideal dipole has its maximum radiation.

This is the normalized reference direction.

Example 3: Half-wave dipole approaching its axis

Now consider an elevation angle approaching 90°.

The converted angle approaches:

θ = 0 ^∘

This is the antenna element-axis direction.

The ideal dipole radiation pattern approaches a null in this direction. Consequently, normalized field and relative power approach zero, while the attenuation approaches a very large negative dB value.

Example 4: Quarter-wave monopole

For the quarter-wave monopole, the calculator models the ideal pattern above an ideal ground plane.

This makes the calculator useful for understanding the basic directional characteristics of a vertical monopole without attempting to model every property of a physical installation.

What This Calculator Does Not Model

The calculator is intentionally simplified.

It evaluates ideal mathematical patterns rather than performing a full electromagnetic simulation.

Real antenna radiation can be influenced by many factors that are outside the calculator's model.

These include:

• Physical antenna construction
• Antenna mounting
• Ground conductivity
• Ground-plane size
• Radials
• Nearby buildings
• Trees
• Towers and other structures
• Terrain
• Feedline interaction
• Reflections
• Multipath propagation
• Mutual coupling
• Installation height
• Other conductive objects

For the quarter-wave monopole, the calculator assumes an ideal ground plane. A real ground plane or radial system will not necessarily behave exactly like this theoretical reference.

Therefore, the calculated pattern should be used for theoretical analysis and relative directional comparison, not as a precise prediction of a particular installed antenna.

Antenna Radiation Pattern vs. Antenna Gain

Radiation pattern and antenna gain are related concepts, but they are not the same thing.

Radiation pattern

A radiation pattern describes how an antenna's radiation varies with direction.

Antenna gain

Antenna gain describes the directional performance of an antenna relative to a specified reference and incorporates the antenna's efficiency characteristics.

This calculator focuses on normalized directional behavior.

For that reason:

A normalized field strength of 1 does not mean an antenna has a gain of 1 dBi.

Similarly, 100% relative radiated power does not mean the antenna has 100% radiation efficiency.

When the calculator displays 0 dB, it means the selected direction corresponds to the normalized pattern maximum.

It does not represent antenna gain, transmitter output, or radiation efficiency.

Common Mistakes When Using an Antenna Radiation Pattern Calculator

1. Confusing elevation angle with element-axis angle

The calculator accepts elevation from the horizon, but the mathematical expression uses an angle from the antenna element axis.

Remember:

θ = 90 ^∘ − α

2. Treating normalized power as actual power

A relative power value is a ratio.

It does not directly represent watts, milliwatts, or transmitter output power.

3. Assuming an ideal pattern represents every real installation

Real antennas are affected by their environment. An ideal mathematical pattern cannot capture all installation effects.

4. Confusing field percentage with power percentage

Field strength must be squared to obtain relative power:

P = F²

A 50% normalized field therefore corresponds to 25% relative power.

5. Thinking 0 dB means no radiation

In this calculator, 0 dB represents the pattern maximum.

A lower relative power produces a negative dB value.

6. Assuming the monopole model represents every ground system

The quarter-wave monopole calculation assumes an ideal ground plane. Real ground systems can produce different results.

Frequently Asked Questions

What is an antenna radiation pattern calculator?

An antenna radiation pattern calculator evaluates how an antenna's ideal radiation varies with direction. This calculator determines normalized field strength, relative radiated power, relative power percentage, and attenuation in dB for isotropic, half-wave dipole, and quarter-wave monopole models.

What is an antenna radiation pattern?

An antenna radiation pattern describes how radiation varies with direction around an antenna. It can be represented using normalized field strength or relative power and can show areas of maximum radiation, reduced radiation, and radiation nulls.

What is the radiation pattern of a half-wave dipole?

An ideal half-wave dipole has a doughnut-shaped three-dimensional radiation pattern. Its maximum radiation occurs broadside to the antenna element, while ideal radiation nulls occur along the element axis.

Where does a half-wave dipole have maximum radiation?

An ideal half-wave dipole has maximum radiation broadside to the antenna element. For a vertically oriented dipole, this corresponds to the horizontal direction.

Where is the radiation null of a dipole?

The ideal half-wave dipole has radiation nulls along its element axis. In this calculator's elevation-angle coordinate system for a vertical element, the element-axis direction corresponds to 90° elevation.

How is relative antenna power calculated?

Relative power is calculated by squaring normalized field strength:

P_relative = ∣F∣²

If normalized field strength is 0.5, the relative power is 0.25.

What does 0 dB mean in an antenna radiation pattern?

In this calculator, 0 dB represents the normalized pattern maximum. It does not mean zero radiation. Directions with lower relative power have negative dB values.

What is normalized antenna field strength?

Normalized field strength expresses the field amplitude relative to the maximum of the selected antenna pattern. The maximum normalized value is 1.

Does this calculator calculate antenna gain?

No. It calculates ideal normalized radiation-pattern quantities. It does not calculate absolute antenna gain, efficiency, or measured radiation performance.

Does the calculator model a real antenna installation?

No. The calculator uses idealized mathematical models. Real antenna patterns can be affected by ground conditions, mounting structures, nearby objects, terrain, reflections, and other environmental factors.

What happens at 90° elevation?

For the dipole and monopole models, 90° elevation corresponds to 0° from the antenna element axis. The ideal model therefore reaches a radiation null in that direction.

What is the difference between field pattern and power pattern?

A field pattern represents relative electromagnetic field amplitude, while a power pattern represents relative power. Power is proportional to the square of field magnitude:

P = ∣F∣²

Related Antenna Calculations

Understanding radiation patterns becomes even more useful when combined with other antenna calculations.

Related topics include:

• Dipole Antenna Calculator
• Half-Wave Dipole Antenna Calculator
• Quarter-Wavelength Antenna Calculator
• Whip Antenna Calculator
• End-Fed Half-Wave Antenna Calculator
• Folded Dipole Antenna Calculator
• Short Dipole Antenna Calculator
• Broadband Dipole Antenna Calculator

You can also explore related antenna concepts such as wavelength, frequency, impedance, antenna gain, radiation efficiency, VSWR, polarization, and antenna matching.

Final Takeaway

The Antenna Radiation Pattern Calculator provides a practical way to explore ideal antenna directionality without performing a full electromagnetic simulation.

It supports three theoretical patterns: isotropic radiator, half-wave dipole, and quarter-wave monopole over an ideal ground plane. By entering an elevation angle from the horizon, the calculator converts that angle into the coordinate system required by the dipole and monopole radiation formula.

For the directional models, the normalized field is calculated using:

F(θ) = cos(π2cosθ)sinθ

The calculator then determines relative power using:

P_relative = ∣F∣²

and expresses the result in dB using:

10log₁₀(P_relative)

The key point is that these values are normalized and idealized. They are useful for understanding antenna theory, comparing directional behavior, and studying radiation patterns, but they should not be interpreted as measurements of a specific real-world antenna.

For practical analysis, select an antenna pattern, enter an elevation angle between 0° and 90°, and use the resulting field, power, percentage, and dB values to understand how the ideal radiation pattern changes with direction.