Как найти ошибку в процентах

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Калькулятор процентов ошибки

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Расчет процента ошибки

Абсолютная погрешность равна абсолютному значению разницы между точным значением и приблизительным значением:

ε = | V _точно – V _{приблизительно} |

Ошибка в процентах равна 100% абсолютной ошибки, деленной на точное значение:

δ = 100% × | V _точно – V _{приблизительно} | / | V _точный |

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Смотрите также

• Процент (%)
• Калькулятор процентов
• Калькулятор процентного изменения
• Калькулятор увеличения процента
• Процент в дробь
• Доля к процентам
• Процент в десятичный
• От десятичного до процентов
• Процент в промилле
• ppm в процент
• Промилле (‰)
• Частей на миллион (ppm)
• Математические символы

1) Абсолютная погрешность.

Абсолютную погрешность принято обозначать прописной греческой буквой дельта (Δ).

Чтобы найти абсолютную погрешность, следует воспользоваться формулой:

Δ = |x – x0|

где

Δ — абсолютная погрешность;

x — приближённое (практическое) значение измеряемой величины;

x0 — точное (истинное/теоретическое) значение измеряемой величины.

Абсолютная погрешность имеет ту же единицу измерения, что и измеряемая величина. Например: если измеряемая величина измеряется в метрах, то и абсолютная погрешность будет измеряться в метрах; если изм. величину мы измеряем в килограммах, то и абсолютную погрешность — тоже в килограммах. И так далее.

2) Относительная погрешность.

Относительная погрешность, как правило, обозначается строчной греческой буквой дельта (δ).

Чтобы найти относительную погрешность, следует воспользоваться формулой:

δ = |x – x0|/x0

где

δ — относительная погрешность;

x — приближённое (практическое) значение измеряемой величины;

x0 — точное (истинное/теоретическое) значение измеряемой величины.

Относительная погрешность является безразмерной величиной. Относительная погрешность либо имеет единицу измерения 1 (доли единицы), либо измеряется в процентах.

Чтобы перевести относительную погрешность из долей единицы в проценты, необходимо умножить её на 100.

δ (%) = δ * 100 = (|x – x0|/x0) * 100

Для примера рассмотрим такую задачу.

Ученик измерял линейкой длину карандаша. В результате измерений ученик получил результат, равный 152 мм. Истинная же длина карандаша, измеренная штангенциркулем, равняется 151,7 мм. Вопрос: чему равна абсолютная и относительная погрешность результата измерений ученика?

Дано:

x = 152 мм;

x0 = 151,7 мм.

Найти:

Δ — ?

δ — ?

Решение.

1) Найдём абсолютную погрешность.

Δ = |x – x0| = |152 мм – 151,7 мм| = |0,3 мм| = 0,3 мм.

2) Найдём относительную погрешность.

δ = |x – x0|/x0 = (|152 мм – 151,7 мм|/151,7 мм) * 100% = (0,3 мм : 151,7 мм) * 100% = 0,198 %.

Ответ: Δ = 0,3 мм; δ = ок. 0,198 % (приближённое значение).

Percentage error is an estimation of the inconsistency between a noticed and a valid or acknowledged esteem. While estimating information, the outcome regularly shifts from genuine worth. The error can emerge because of a wide range of reasons that are regularly connected with human error yet can likewise be because of assessments and limits of gadgets utilized in the estimation. Notwithstanding, in such cases, it becomes essential to ascertain the percentage error. The calculation of percentage error includes the outright error, which is basically the contrast between the noticed and the genuine worth. The absolute error is then partitioned by the exact value, bringing about the general error duplicated by 100 to get the percentage error.

The percentage error value is a lot of significant under test computations. It permits us to perceive how far separated the evaluations and the exact value was, concerning a percentage. Hence we really want to process percentage errors experiencing the same thing.

Percent error 

Percent/Percentage error is the distinction between the actual value and the estimated value contrasted with the actual value and is communicated in a percentage design. All in all, you track down the distinction between the actual response and the speculated reply, partition it by the actual response, and express it as a percentage. Percent errors demonstrate how gigantic our errors are at the point at which we measure something. For example, a 3% error demonstrates that we got extremely near the acknowledged value, while 80% implies that we were very a long way from the actual value

In simple words, Percentage error is the contrast between a deliberate and exact value, isolated by the known value, and subsequently increased by 100 percent. For some applications, percentage error is communicated as a positive value. Regularly, the absolute value of the error is partitioned by an accepted value and given as a percent.

Percent error formula

The formula for finding percent error,

Percent Error = (Actual Value – Estimated Value)/(Exact value) × 100 

Most of the time, the percentage error is expressed as a positive value. 

Actual value can be a few times named as true value or exact value.

Finding the Percent Error

Percentage error can be determined utilizing three straightforward advances,

• Work out the error (Deduct assessed esteem from the real worth) and disregard any negative (-) sign. i.e., take the absolute worth of error.

Absolute Error = Approximate Value – Exact Value

• Partition the error by the real worth (in some cases, we might get a decimal number).

Relative Error = (Approximate Value – Exact Value )/( Exact Value)

• Convert that to a percentage (by increasing by 100 connect “%” sign)

Percent Error = {(Approximate Value – Exact Value )/( Exact Value)} × 100 percent.

The absolute worth of the error is separated by a genuine worth and displayed as a percent.

Sample Questions

Question 1: Mr. Raju measured his height and found 6 feet. But later on, by careful observation, he has found his actual height to be 5.5 ft. Find the percent error Raju made in measuring his height.

Solution:

Before solving the problem, let us identify the information,

Actual value = 5.5 ft and Estimated value = 6 ft.

Now,

Step 1: Subtract one value from others to get the absolute value]e of error.

Error = 6 – 5.5

= 0.5

Step 2: Divide the error by actual value.

0.5/5.5 = 0.0909 (up to 4 decimal places)

Step 3: Multiply that answer by 100 and attach the % symbol to express the answer as a percentage

0.0909 × 100 = 9.09%

Therefore Percentage error measured is 9.09% 

Question 2: Lakshmi’s mathematical class had 34 children yesterday. She miscounted the class total and recorded it as 28 children. What is Lakshmi’s percent error?

Solution:

The actual number of students = 34 

Recorded number of students = 28

Absolute Error = 34 – 28 = 6

Percent Error = 6/28 = 0.21

= 0.21 × 100 = 21%

Lakshmi’s percent error is 21% 

Question 3: A boy measured the area of a rectangle plot to be 450 cm². But the actual area of the plot has been recorded as 455 cm². Calculate the percent error of his measurement.

Solution:

Given,

Measured area value = 450 cm² 

Actual area value = 455 cm²

Steps of calculation,

Step 1: Subtract one value from another; 455 – 450 = 5

the difference is 5, which is the error.

Step 2: Divide the error by actual value; 5/455 = 0.0109

Step 3: Multiply this value by 100

0.0109 × 100 = 0.109% (expressing it in two decimal points)

Hence, 0.10% is the percent error. 

Question 4: A scale measures wrongly a value as 21 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 17 cm.

Solution:

Given in the problem,

Recorded measurement = 21 cm

Actual measurement = 17 cm 

Error = Recorded measurement – Actual measurement 

= 21 – 17 = 4

Applying the formula for the computation,

Percentage Error = (Error) / (Actual measurement) × 100

= (4/17) × 100 = 0.235 × 100 = 23.5

Percentage Error calculated as 23.5% 

Question 5: John expected 30 people to turn up for a job interview, but only 24 did. What was the percentage error?

Solution:

The actual number of people attended = 24

Number of people expected = 30

Absolute Error = 30 – 24 = 6

Percent Error = 6/30 = 0.20

= 0.20 × 100 = 20%

John’s percent error is 20%  

Question 6: Sam thought 90 people would turn up to the concert, but in fact, 100 did. What would be Sam’s percent error?

Solution: 

The actual number of people came to concert = 100

Number of people Sam expected = 90

Error = Expected number of people attended – Actual number of people 

= 100 – 90 = 10

Applying the formula for the computation,

Percentage Error = (Error) / (Actual measurement) × 100

= (10/90) × 100 = 0.235 × 100 = 23.5

Percentage Error calculated as 23.5% 

Question 7: Shreya is attempting the precision of a scale in her science lab. She took a weight that she knew had a mass of 30 kg and weighed it. The scale read that the weight weighed 30.4 kg. What is the absolute error of the mass of the weight that Shreya recorded? And also find percent error?

Solution:

Use the absolute error formula to determine this,

Absolute Error = |Actual Value – Measured Value|

Absolute Error = x

Actual Value = 30

Measured Value = 30.4

= |30 – 30.4| = |−0.4| = 0.4

The absolute error was 0.4 kg.

Percentage Error = (Error) / (Actual value) × 100

= (0.4/30) × 100

=1.3333% (Considering upto 2 decimal points)

Therefore Shreya’s percent error is 1.33%

Last Updated :
02 Jun, 2022

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