数学

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Linear Interpolation Calculator.

Interpolate y at x between two known points.

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输入数值

输入时结果会更新。

02 / 答案

Known x₁

Known y₁

Known x₂

Known y₂

Target x

Interpolated y

40.000000

Interpolation fraction

0.400000

Results update automatically as you type.

Use Cases

Estimate values between data points

Use this calculator to find an approximate y value for a given x when you only have two known points, such as in tables or graphs.

Example: Given (0, 10) and (10, 20), find y at x=5 → y=15.

Fill in missing data in experiments

When you have two measured data points and need a quick estimate for an intermediate condition, this tool provides a fast linear approximation.

Example: If temperature at 2 PM is 20°C and at 4 PM is 24°C, estimate at 3 PM → 22°C.

Frequently Asked Questions

What is linear interpolation?: Linear interpolation estimates a value between two known data points by assuming a straight line between them. It uses the formula y = y₁ + (y₂ - y₁) * (x - x₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the known points and x is the target x.
Can I use this calculator for extrapolation?: No, this calculator is designed for interpolation only. It assumes the target x lies between x₁ and x₂. If the target x is outside that range, the result would be an extrapolation, which is not supported by this tool.
What if x₁ equals x₂?: If x₁ equals x₂, the denominator in the interpolation formula becomes zero, making the calculation undefined. The calculator will not provide a valid result in that case. Ensure the two x values are different.

Tips & Common Mistakes

Tips

Ensure the target x is between x₁ and x₂ for accurate interpolation.
Double-check that x₁ and x₂ are not equal to avoid division by zero.
Use consistent units for x and y values to get meaningful results.
For non-linear data, linear interpolation may be less accurate; consider other methods.

Common Mistakes to Avoid

Entering x₁ and x₂ in the wrong order – the calculator works regardless, but it's good practice to keep them consistent.
Using the calculator for extrapolation when the target x is outside the known range.
Forgetting to input all four known values – the calculator needs both points to compute the result.

Last updated: August 13, 2026

Use Cases

Estimate values between data points

Use this calculator to find an approximate y value for a given x when you only have two known points, such as in tables or graphs.

Example: Given (0, 10) and (10, 20), find y at x=5 → y=15.

Fill in missing data in experiments

When you have two measured data points and need a quick estimate for an intermediate condition, this tool provides a fast linear approximation.

Example: If temperature at 2 PM is 20°C and at 4 PM is 24°C, estimate at 3 PM → 22°C.

Frequently Asked Questions

What is linear interpolation?

Linear interpolation estimates a value between two known data points by assuming a straight line between them. It uses the formula y = y₁ + (y₂ - y₁) * (x - x₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the known points and x is the target x.

Can I use this calculator for extrapolation?

No, this calculator is designed for interpolation only. It assumes the target x lies between x₁ and x₂. If the target x is outside that range, the result would be an extrapolation, which is not supported by this tool.

What if x₁ equals x₂?

If x₁ equals x₂, the denominator in the interpolation formula becomes zero, making the calculation undefined. The calculator will not provide a valid result in that case. Ensure the two x values are different.

Tips & Common Mistakes

Tips

Ensure the target x is between x₁ and x₂ for accurate interpolation.
Double-check that x₁ and x₂ are not equal to avoid division by zero.
Use consistent units for x and y values to get meaningful results.
For non-linear data, linear interpolation may be less accurate; consider other methods.

Common Mistakes to Avoid

Entering x₁ and x₂ in the wrong order – the calculator works regardless, but it's good practice to keep them consistent.
Using the calculator for extrapolation when the target x is outside the known range.
Forgetting to input all four known values – the calculator needs both points to compute the result.

Use Cases

Estimate values between data points

Use this calculator to find an approximate y value for a given x when you only have two known points, such as in tables or graphs.

Example: Given (0, 10) and (10, 20), find y at x=5 → y=15.

Fill in missing data in experiments

When you have two measured data points and need a quick estimate for an intermediate condition, this tool provides a fast linear approximation.

Example: If temperature at 2 PM is 20°C and at 4 PM is 24°C, estimate at 3 PM → 22°C.

Frequently Asked Questions

What is linear interpolation?

Can I use this calculator for extrapolation?

What if x₁ equals x₂?

Tips & Common Mistakes

Tips

Ensure the target x is between x₁ and x₂ for accurate interpolation.
Double-check that x₁ and x₂ are not equal to avoid division by zero.
Use consistent units for x and y values to get meaningful results.
For non-linear data, linear interpolation may be less accurate; consider other methods.

Common Mistakes to Avoid

Entering x₁ and x₂ in the wrong order – the calculator works regardless, but it's good practice to keep them consistent.
Using the calculator for extrapolation when the target x is outside the known range.
Forgetting to input all four known values – the calculator needs both points to compute the result.