Free & Instant — No Signup Required

Hazard Ratio Calculator

The Hazard Ratio Calculator computes the ratio of hazard rates between two groups in survival analysis. Interpret hazard ratios from clinical trials, Kaplan-Meier curves, and Cox proportional hazards models for treatment effectiveness.

Hazard Ratio Calculator — Live Preview
Hazard Ratio
—
A
B
⚖️
Proportion Solver
A : B = C : D — Enter any 3 values
:
=
:
📊
Results
Visual ratio breakdown
Solved Proportion
—
Simplified
—
Percentages
—
Decimal
—
Fraction
—
Visual Ratio
A
B
Part A: —
Part B: —
    ✨
    Ratio Simplifier
    Reduce any ratio to its simplest form
    :
    📊
    Simplified Result
    Reduced to lowest terms
    Simplified Ratio
    —
    GCD Used
    —
    Percentages
    —
    Decimal Ratio
    —
    Fraction
    —
    Visual Ratio
    A
    B
    Part A: —
    Part B: —
      📐
      Ratio Scaler
      Multiply a ratio by a scale factor
      :
      ×
      📊
      Scaled Result
      Ratio after scaling
      Scaled Ratio
      —
      Original
      —
      Factor
      —
      Percentages
      —
      Simplified
      —
      Visual Ratio
      A
      B

        🕐 Recent Calculations

        📭
        No calculations yet. Start computing above!

        What is a Hazard Ratio?

        A hazard ratio (HR) compares the instantaneous rate of an event (death, disease recurrence, failure) between two groups at any point in time. An HR of 0.70 means the treatment group has 30% lower hazard (risk at any given moment) than the control group throughout the study period.

        Hazard ratios are derived from Cox proportional hazards regression and are the standard measure in survival analysis. Unlike relative risk (which compares cumulative probabilities), HR compares instantaneous rates and handles censored data (patients lost to follow-up).

        Formulas & Equations Used

        This Hazard Ratio Calculator uses the following core equations:

        1 Hazard Ratio ▼
        HR = Hazard Rate (Treatment) / Hazard Rate (Control)

        HR < 1 favors treatment. HR > 1 favors control. HR = 1 means no difference.

        2 Median Survival Ratio (approximation) ▼
        Survival Ratio ≈ 1 / HR

        If HR = 0.5, the treatment group lives approximately twice as long (median survival ratio = 2).

        3 Risk Reduction from HR ▼
        Risk Reduction = (1 - HR) × 100%

        HR = 0.65: Risk reduction = (1-0.65) × 100 = 35% reduction in the event rate.

        How to Use This Hazard Ratio Calculator

        Follow these 3 simple steps:

        1

        Enter Your Values

        Type the known values into the input fields above. The Hazard Ratio Calculator accepts any positive numbers.

        2

        Choose Calculation Mode

        Select Solve, Simplify, or Scale mode in the calculator. Each applies different equations to your inputs.

        3

        View Results

        Click Calculate to see your answer with a visual ratio bar, pie chart, and step-by-step solution breakdown.

        Example Problems & Step-by-Step Solutions

        Here are 3 worked examples using this Hazard Ratio Calculator:

        Example 1 Cancer trial: HR = 0.72 for new drug
        1 Risk reduction = (1 - 0.72) × 100 = 28%
        2 The new drug reduces death risk by 28%
        3 If 95% CI: (0.55, 0.95) — significant (doesn't cross 1.0)
        ✓ 28% reduction in death risk (HR = 0.72, significant)
        Example 2 Compare two treatments: HR = 1.15
        1 HR > 1.0 favors the control group
        2 Treatment group has 15% higher hazard
        3 95% CI: (0.88, 1.50) — crosses 1.0, not significant
        ✓ HR = 1.15, not statistically significant
        Example 3 Estimate median survival improvement
        1 Control median survival: 12 months
        2 HR = 0.60 for new treatment
        3 Estimated treatment median: 12 / 0.60 ≈ 20 months
        4 Improvement: approximately 8 months
        ✓ Treatment extends median survival ~8 months

        Frequently Asked Questions

        What does a hazard ratio of 0.5 mean? ▼

        HR = 0.5 means the treatment group has half the instantaneous risk of the event at any time point compared to the control group. This represents a 50% risk reduction and roughly doubles the time-to-event.

        How is hazard ratio different from relative risk? ▼

        Relative risk compares cumulative event probabilities over the entire study. Hazard ratio compares instantaneous event rates at any point in time. HR handles censored data and time-varying exposure, while RR cannot.

        When is a hazard ratio statistically significant? ▼

        When its 95% confidence interval does not include 1.0. HR = 0.70 with CI (0.50, 0.98) is significant. HR = 0.70 with CI (0.45, 1.10) is not significant because the CI crosses 1.0.

        What is the proportional hazards assumption? ▼

        Cox regression assumes the HR remains constant over time. If the treatment is very effective early but less so later, the proportional hazards assumption is violated. Schoenfeld residuals test this assumption.

        Can hazard ratio be used with Kaplan-Meier curves? ▼

        HR is typically derived from Cox regression, not directly from Kaplan-Meier curves. However, the log-rank test p-value from KM analysis can assess significance, and HR provides the effect size.

        Learn About Ratios

        What is a ratio?

        A ratio is a comparison between two or more quantities showing the relative size of one to another. Written as A : B, it means 'for every A units of the first quantity, there are B units of the second.' For example, a ratio of 3 : 4 means for every 3 parts of A, there are 4 parts of B. Ratios are used in cooking, construction, finance, science, and everyday life.

        How do I solve a proportion?

        A proportion is an equation that says two ratios are equal: A : B = C : D. To solve for a missing value, use cross-multiplication. If D is unknown: D = (B × C) / A. This works because in equal ratios, the cross products are always equal: A × D = B × C. Our Proportion Solver does this automatically — just enter any 3 values and it finds the 4th.

        How do I simplify a ratio?

        To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, 24 : 36 — the GCD of 24 and 36 is 12. So 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving the simplified ratio 2 : 3. Our Simplifier automatically finds the GCD and reduces your ratio to its lowest terms.

        What is ratio scaling and when is it useful?

        Scaling a ratio means multiplying both parts by the same factor to create an equivalent, larger (or smaller) ratio. For instance, scaling 2 : 5 by a factor of 3 gives 6 : 15. This is extremely useful for recipes (tripling a recipe), construction (scaling blueprints), mixing solutions, or any scenario where you need to maintain the same proportion at a different magnitude.

        What's the difference between a ratio and a fraction?

        A ratio A : B compares two quantities to each other (part-to-part), while a fraction A/B typically represents a part-to-whole relationship. However, any ratio can be expressed as a fraction: 3 : 4 is equivalent to 3/4 = 0.75. The key difference is context — ratios compare quantities side-by-side, while fractions represent a portion of a total.