Error Interval Calculator 2026
Find the upper and lower bounds (limits of accuracy) for any rounded or truncated number. Perfect for GCSE Maths revision and homework.
Measurement Accuracy
Enter your rounded or truncated value to find its error interval
This is the value you have after rounding or truncation.
Rounding finds the nearest value, while truncation simply cuts off digits.
Error Interval Results
Lower and upper bounds for your measurement
Enter your value and rounding method above, then click Calculate Bounds to see the error interval.
Error Intervals for Common Scenarios
Examples of how to write error intervals for different types of rounding and truncation.
| Given Value | Rounding/Truncation | Error Interval | Explanation |
|---|---|---|---|
| 8 | Rounded to nearest 1 | 7.5 ≤ x < 8.5 | Half-unit is 0.5 |
| 5.6 | Rounded to 1 d.p. | 5.55 ≤ x < 5.65 | Half-unit is 0.05 |
| 120 | Rounded to nearest 10 | 115 ≤ x < 125 | Half-unit is 5 |
| 3.7 | Truncated to 1 d.p. | 3.7 ≤ x < 3.8 | Starts at given value |
| 4200 | Rounded to nearest 100 | 4150 ≤ x < 4250 | Half-unit is 50 |
| 0.84 | Truncated to 2 d.p. | 0.84 ≤ x < 0.85 | Next value in 0.01s |
Error Interval FAQ
Understand the core concepts of limits of accuracy, rounding, and truncation for your GCSE Maths exam.
An error interval is the range of possible values that a number could have been before it was rounded or truncated. It defines the limits of accuracy for a given measurement. The interval is written as 'lower bound ≤ true value < upper bound' [[1]].
To find the error interval for a rounded number: 1) Identify the unit of rounding (e.g., nearest 0.1). 2) Calculate half of this unit (the margin of error). 3) Subtract the margin from the given value to get the lower bound. 4) Add the margin to get the upper bound. The error interval is then [lower bound, upper bound) [[9]].
For a rounded number, the error interval is symmetric around the given value (e.g., 5.6 rounded to 1 d.p. has an interval of 5.55 ≤ x < 5.65). For a truncated number, the error interval starts at the given value and goes up to the next possible value in the unit of truncation (e.g., 5.6 truncated to 1 d.p. has an interval of 5.6 ≤ x < 5.7).
Error intervals are a key topic in GCSE Maths (Number) because they teach students about the limits of accuracy in measurements. Understanding bounds is crucial for estimating the maximum and minimum possible values in calculations involving measured quantities, which is a common exam question.
An error interval is written using inequalities. For a value 'x' that has been rounded, the standard notation is 'lower bound ≤ x < upper bound'. This shows that the true value can be equal to the lower bound but must be less than the upper bound [[10]].