Loss Factor tan delta Calculator

Core definition

• tan δ = E″ / E′ (or G″ / G′) for viscoelastic modulus data.
• tan δ = ε″ / ε′ for dielectric loss tangent.
• tan δ = tan(δ), where δ is the phase lag between input and response.
• tan δ ≈ 1 / Q when Q is defined as stored-to-lost energy per radian.

Derived quantities

• Loss factor η is commonly taken as η = tan δ.
• Q = 1 / tan δ (useful for resonance sharpness comparisons).
• ΔW / W_stored ≈ 2π·tan δ estimates energy loss per cycle.

These relations assume linear response and consistent measurement conditions.

1. Select the method that matches your measurement output.
2. Enter the requested inputs with consistent units and signs.
3. Press Calculate to show results above the form.
4. Review tan δ, loss factor, Q, and energy loss ratio.
5. Use the CSV or PDF buttons to export the latest result.

If your phase angle is small, tan δ ≈ δ (radians) can be a quick check.

1) What tan delta represents

Loss factor, written as tan δ, is a dimensionless measure of damping. It compares the dissipative part of a cyclic response to the energy-storing part. A higher tan δ generally means more heat generation and broader resonance peaks, while a lower tan δ indicates a more elastic, lower-loss response.

2) Typical ranges in common materials

In many polymers near room temperature, tan δ often falls between about 0.01 and 0.30, depending on frequency and formulation. Fiber-reinforced composites may show lower values (for example 0.005 to 0.08) in stiff directions. Near glass transition, tan δ can rise significantly and shift with frequency.

3) Modulus method data from dynamic tests

For dynamic mechanical measurements, the calculator uses tan δ = E″/E′ (or G″/G′). If E′ = 1.20×10⁹ and E″ = 6.50×10⁷, tan δ ≈ 0.054. The unit choice does not affect the ratio, as long as both moduli share the same unit basis.

4) Dielectric loss tangent interpretation

For dielectric data, tan δ = ε″/ε′ compares loss and storage in the electric field response. As an example, ε′ = 3.20 and ε″ = 0.12 gives tan δ = 0.0375. This value can increase with temperature or at frequencies where dipolar relaxation is active.

5) Phase angle method and small-angle checks

If you know the phase lag δ in degrees, tan δ = tan(δ). A 3° lag produces tan δ ≈ 0.0524. For quick validation at small lags, δ in radians is close to tan δ; 3° is about 0.05236 radians, matching the computed value closely.

6) Linking losses to Q factor

Quality factor Q is often used in resonance studies. Under common definitions, tan δ ≈ 1/Q. If Q = 100, tan δ = 0.01. If Q = 20, tan δ = 0.05. This relation helps compare damping across test setups when Q is reported instead of complex moduli.

7) Energy loss per cycle estimate

A convenient metric is the energy loss ratio per cycle, ΔW/W_stored ≈ 2π·tan δ. For tan δ = 0.05, the estimate is about 0.314, meaning roughly 31% of stored energy is dissipated each cycle. For tan δ = 0.01, it drops to about 6.28%.

8) Practical reporting and comparison tips

Always report the frequency, temperature, and strain or field amplitude used to obtain tan δ. Values can shift notably across decades of frequency. When comparing materials, keep conditions consistent and avoid mixing shear and tensile data unless you state the test mode clearly.

1) Is loss factor always equal to tan delta?

In many linear, small-signal measurements, loss factor is taken as tan δ. Some fields use alternative definitions, so it is best to state the exact formula and measurement method alongside the reported value.

2) Can tan delta be negative?

For passive materials under standard conventions, tan δ should be non‑negative. Negative values usually indicate sign conventions, calibration issues, or phase reference errors in the measurement chain.

3) Why does tan delta change with frequency?

Loss mechanisms are time‑dependent. Molecular relaxations, interfacial friction, and conduction losses respond differently at different frequencies, shifting the balance between storage and dissipation, and changing tan δ.

4) What is a “good” tan delta value?

It depends on the goal. Low-loss resonators often target tan δ below 0.01, while vibration damping layers may prefer 0.05 to 0.30, especially near the operating temperature and frequency band.

5) How accurate is ΔW/Wstored ≈ 2π·tan delta?

It is a practical estimate for small-to-moderate losses and near‑sinusoidal steady behavior. At very high damping or strongly nonlinear response, the relationship can deviate from measured energy loss.

6) Which modulus should I use, E or G?

Use the modulus reported by your test: E′/E″ for tensile or flexural dynamic tests, and G′/G″ for shear tests. The ratio is what matters; do not mix modes in a single calculation.

7) What inputs should I export for reports?

Include the method, raw inputs, tan δ, Q, derived phase angle, and test conditions such as frequency and temperature. This supports traceability and makes comparisons meaningful across datasets.