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Damping Ratio or Damping Factor Calculator

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✖Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.ⓘ Damping Coefficient [c]
+10%
-10%
✖Mass is defined as the force exerted by an object due the effect of gravity on any surface.ⓘ Mass [m]
+10%
-10%
✖Spring Constant is the displacement of the spring from its equilibrium position.ⓘ Spring Constant [Kspring]
+10%
-10%
✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio or Damping Factor [ζ]
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Formula
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Damping Ratio or Damping Factor

Formula
`"ζ" = "c"/(2*sqrt("m"*"K"_{"spring"}))`

Example
`"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))`

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Damping Ratio or Damping Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
ζ = c/(2*sqrt(m*Kspring))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Damping Coefficient - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Mass - (Measured in Kilogram) - Mass is defined as the force exerted by an object due the effect of gravity on any surface.
Spring Constant - (Measured in Newton per Meter) - Spring Constant is the displacement of the spring from its equilibrium position.
STEP 1: Convert Input(s) to Base Unit
Damping Coefficient: 16 --> No Conversion Required
Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Spring Constant: 51 Newton per Meter --> 51 Newton per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ζ = c/(2*sqrt(m*Kspring)) --> 16/(2*sqrt(35.45*51))
Evaluating ... ...
ζ = 0.188146775281754
STEP 3: Convert Result to Output's Unit
0.188146775281754 --> No Conversion Required
FINAL ANSWER
0.188146775281754 ≈ 0.188147 <-- Damping Ratio
(Calculation completed in 00.004 seconds)
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Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
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19 Fundamental Parameters Calculators

Angle of Asymptotes
Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
Bandwidth Frequency given Damping Ratio
Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive Feedback Gain
Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))
Closed Loop Negative Feedback Gain
Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
Damping Ratio or Damping Factor
Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Resonant Peak
Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Transfer Function for Closed and Open Loop System
Go Transfer Function = Output of System/Input of System
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Go Closed-Loop Gain = 1/Feedback Factor
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

25 Control System Design Calculators

Time Response in Overdamped Case
Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Time Response of Critically Damped System
Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
Bandwidth Frequency given Damping Ratio
Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
Rise Time given Damping Ratio
Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Time Response in Undamped Case
Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
First Peak Undershoot
Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Number of Oscillations
Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Delay Time
Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Time Period of Oscillations
Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Setting Time when Tolerance is 2 Percent
Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Peak Time
Go Peak Time = pi/Damped Natural Frequency
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)
Rise Time given Delay Time
Go Rise Time = 1.5*Delay Time

12 Modelling Parameters Calculators

Angle of Asymptotes
Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
Bandwidth Frequency given Damping Ratio
Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Damping Ratio or Damping Factor
Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Resonant Peak
Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

Damping Ratio or Damping Factor Formula

Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
ζ = c/(2*sqrt(m*Kspring))

How is damping ratio used?

To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping required to reach critical damping. The formula for the damping ratio is used for the mass-spring-damper model.

How is damping factor obtained?

The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient. The damping ratio is dimensionless, being the ratio of two coefficients of identical units.

How to Calculate Damping Ratio or Damping Factor?

Damping Ratio or Damping Factor calculator uses Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) to calculate the Damping Ratio, Damping Ratio or Damping Factor is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. Damping Ratio is denoted by ζ symbol.

How to calculate Damping Ratio or Damping Factor using this online calculator? To use this online calculator for Damping Ratio or Damping Factor, enter Damping Coefficient (c), Mass (m) & Spring Constant (Kspring) and hit the calculate button. Here is how the Damping Ratio or Damping Factor calculation can be explained with given input values -> 0.188147 = 16/(2*sqrt(35.45*51)).

FAQ

What is Damping Ratio or Damping Factor?
Damping Ratio or Damping Factor is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator and is represented as ζ = c/(2*sqrt(m*Kspring)) or Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system, Mass is defined as the force exerted by an object due the effect of gravity on any surface & Spring Constant is the displacement of the spring from its equilibrium position.
How to calculate Damping Ratio or Damping Factor?
Damping Ratio or Damping Factor is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator is calculated using Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). To calculate Damping Ratio or Damping Factor, you need Damping Coefficient (c), Mass (m) & Spring Constant (Kspring). With our tool, you need to enter the respective value for Damping Coefficient, Mass & Spring Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Damping Ratio?
In this formula, Damping Ratio uses Damping Coefficient, Mass & Spring Constant. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Damping Ratio = Actual Damping/Critical Damping
  • Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
  • Damping Ratio = Actual Damping/Critical Damping
  • Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
  • Damping Ratio = Actual Damping/Critical Damping
  • Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
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