Residual Error Calculator

✖Observed value is the value which the observer notes during surveying.ⓘ Observed Value [x]			+10% -10%
✖Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.ⓘ Most Probable Value [MPV]			+10% -10%

✖Residual error is the difference between the most probable value of a quantity and its observed value.ⓘ Residual Error [r]

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Formula

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Residual Error

Formula

`"r" = "x"-"MPV"`

Example

`"80"="159"-"79"`

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Residual Error Solution

STEP 0: Pre-Calculation Summary

Formula Used

Residual Error = Observed Value-Most Probable Value
r = x-MPV
This formula uses 3 Variables

Variables Used

Residual Error - Residual error is the difference between the most probable value of a quantity and its observed value.
Observed Value - Observed value is the value which the observer notes during surveying.
Most Probable Value - Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.

STEP 1: Convert Input(s) to Base Unit

Observed Value: 159 --> No Conversion Required
Most Probable Value: 79 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = x-MPV --> 159-79

Evaluating ... ...

r = 80

STEP 3: Convert Result to Output's Unit

80 --> No Conversion Required

FINAL ANSWER

80 <-- Residual Error

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 21 Theory of Errors Calculators

Standard Error of Function where variables are Subjected to Addition

Go Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2)

Most Probable Value with Different Weightage

Go Most Probable Value = add(Weightage*Measured Quantity)/add(Weightage)

Standard Deviation of Weighted Observations

Go Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1))

Standard Deviation used for Survey Errors

Go Standard Deviation = sqrt(Sum of Square of Residual Variation/(Number of Observations-1))

Mean Error given Specified Error of Single Measurement

Go Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations))

Standard Error of Mean of Weighted Observations

Go Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage)

Probable Error of Mean

Go Probable Mean of Error = Probable Error in Single Measurement/(Number of Observations^0.5)

Variance of Observations

Go Variance = Sum of Square of Residual Variation/(Number of Observations-1)

Mean Error given Sum of Errors

Go Error of Mean = Sum of Errors of Observations/Number of Observations

Most Probable Value with Same Weightage for Observations

Go Most Probable Value = Sum of Observed Values/Number of Observations

Residual Variation given Most Probable Value

Go Residual Variation = Measured Value-Most Probable Value

Most Probable Value given Residual Error

Go Most Probable Value = Observed Value-Residual Error

Observed Value given Residual Error

Go Observed Value = Residual Error+Most Probable Value

Residual Error

Go Residual Error = Observed Value-Most Probable Value

Observed Value given Relative Error

Go Observed Value = True Error/Relative Error

True Error given Relative Error

Go True Error = Relative Error*Observed Value

Relative Error

Go Relative Error = True Error/Observed Value

Observed Value given True Error

Go Observed Value = True Value-True Error

True Value given True Error

Go True Value = True Error+Observed Value

True Error

Go True Error = True Value-Observed Value

Most Probable Error given Standard Deviation

Go Most Probable Error = 0.6745*Standard Deviation

Residual Error Formula

Residual Error = Observed Value-Most Probable Value
r = x-MPV

What are the Sources of Error?

Natural errors: These result from the temperature, refraction, obstacles to measurements, magnetic declination, etc. For example, the length of a steel tape varies with changes in temperature. Such sources of error are beyond the control of the surveyor.

How to Calculate Residual Error?

Residual Error calculator uses Residual Error = Observed Value-Most Probable Value to calculate the Residual Error, The Residual Error is the difference between the most probable value of a quantity and its observed value. The most probable value of a quantity is the one which has more chances of being true than has any other. Residual Error is denoted by r symbol.

How to calculate Residual Error using this online calculator? To use this online calculator for Residual Error, enter Observed Value (x) & Most Probable Value (MPV) and hit the calculate button. Here is how the Residual Error calculation can be explained with given input values -> 80 = 159-79.

FAQ

What is Residual Error?

The Residual Error is the difference between the most probable value of a quantity and its observed value. The most probable value of a quantity is the one which has more chances of being true than has any other and is represented as r = x-MPV or Residual Error = Observed Value-Most Probable Value. Observed value is the value which the observer notes during surveying & Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.

How to calculate Residual Error?

The Residual Error is the difference between the most probable value of a quantity and its observed value. The most probable value of a quantity is the one which has more chances of being true than has any other is calculated using Residual Error = Observed Value-Most Probable Value. To calculate Residual Error, you need Observed Value (x) & Most Probable Value (MPV). With our tool, you need to enter the respective value for Observed Value & Most Probable Value and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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